Apparatus and method for optical code delay reflectance measurement (OCoDR)

Abstract

An apparatus and method for optical code delay reflectometry (OCoDR) is disclosed. The apparatus includes a modulator, a receiver, and a control circuit. The modulator is configured to receive incident electromagnetic (EM) radiation of a substantially fixed frequency generated by one or more EM radiation sources. The incident EM radiation includes continuous wave EM radiation. The modulator is configured to impart a sequence to the amplitude, phase, or both of the incident EM radiation to generate the modulated EM radiation. The modulated EM radiation includes continuous wave EM radiation. The receiver is configured to receive a reference EM radiation. The receiver is also configured to receive reflected EM radiation from the optical system in response to the modulated EM radiation, and generate an interferometric EM radiation in response to the reference EM radiation and the reflected EM radiation. The receiver is further configured to generate a continuous interferogram in response to the interferometric EM radiation.

Description

[Technical Field]

[0001] Priority Claim This application asserts the interests under 119(e) of U.S. Patent Act Section 119(e) of U.S. Provisional Patent Application No. 63 / 203363, filed on 20 July 2021, which is incorporated herein by this reference in its entirety.

[0002] This disclosure generally relates to apparatus and methods for optical sensing, and more specifically to optical sensing using continuous-wave electromagnetic (EM) radiation.

[0003] Description of research and development funded by the federal government. This invention was developed with government support under contract number DE-SC0020755 from the U.S. Department of Energy and contract number N6833520C0183 from the U.S. Department of the Navy. The government has certain rights to this invention. [Background technology]

[0004] Optical systems, such as optical fibers, can be used as sensors in a variety of applications. For example, modulation of mechanical stress in an optical system due to strain or temperature fluctuations can alter the measurable optical properties of the system. [Overview of the project] [Means for solving the problem]

[0005] This disclosure concludes with claims that specifically designate and expressly assert certain embodiments, but various features and advantages of embodiments within the scope of this disclosure may be more readily apparent from the following description when read in conjunction with the accompanying drawings. [Brief explanation of the drawing]

[0006] [Figure 1] This is a block diagram of a measurement system according to several embodiments. [Figure 2]This is a signal processing diagram illustrating a multiplier-accumulator architecture for performing OCoDR in several embodiments. [Figure 3] This is a signal processing diagram illustrating frequency domain architectures for performing OCoDR according to several embodiments. [Figure 4] This is a digital signal processing diagram illustrating Zadoff-Chu sequence architectures for performing OCoDR according to several embodiments. [Figure 5] This plot illustrates an example of the phase derivative of a first-root, zero-shift Zadoff-Chu digital sequence. [Figure 6] This plot illustrates the reflectance of an example of the synthetic system being tested. [Figure 7] Figure 6 is a plot illustrating the phase derivative of the reflector. [Figure 8] This is a plot of the phase derivative of the reflector signal (phase derivative in Figure 7) after digitizing the interferogram with the analog-to-digital converter and multiplying the interferogram with the complex conjugate of the original Zadoff Chu sequence, which was also transmitted to the modulator, before the effects of digital sampling of the signal are fully considered. [Figure 9] This plot illustrates the phase derivatives (frequency) arising from three exemplary reflectors after fully considering the effects of digital sampling of the signal. [Figure 10] This is a diagram showing one representation of a simple phase modulator according to several embodiments. [Figure 11] This is a diagram illustrating one representation of a real modulator (for example, a Mach-Zehnder modulator, but not limited to) according to several embodiments. [Figure 12] This is a collection of plots illustrating digitization, mixing, filtering, and resampling performed on received waveforms, using non-restrictive examples. [Figure 13]This is a diagram of one representation of a complex modulator according to several embodiments. [Figure 14] This is a diagram illustrating one representation of a complex receiver according to several embodiments. [Figure 15] This is a diagram showing one representation of a real receiver according to several embodiments. [Figure 16] This is a collection of plots illustrating digitization, mixing, filtering, and resampling performed on received waveforms, using non-restrictive examples. [Figure 17] This is a functional flowchart of a signal processing scheme suitable for use with a real modulator (for example, the real modulator in Figure 11) and a real receiver (for example, the real receiver in Figure 15). [Figure 18] This is a diagram illustrating one representation of a bipolarized complex receiver according to several embodiments. [Figure 19] This is a diagram illustrating one representation of a bipolarized complex modulator according to several embodiments. [Figure 20] This is a functional flowchart for signal processing scheme 2000 suitable for use with polarization diversity OCoDR embodiments. [Figure 21] This plot shows an example of a PRBS sequence according to several embodiments. [Figure 22] Figure 21 is a plot illustrating the cyclic autocorrelation of the PRBS sequence. [Figure 23] This shows plots of interferogram signals in several embodiments. [Figure 24] This plot illustrates the amplitudes of the x and y components of the interferogram signal in several embodiments. [Figure 25] This plot illustrates the cross-section of the interferogram signal between the symbol at 0° and the symbol at 180° in several embodiments. [Figure 26] These plots illustrate the x and y components of the cross-section from 0° to 180° and its return cross-section, using an MZ modulator approach for ψ=25° according to several embodiments. [Figure 27] This is a side view of an example of an optical fiber. [Figure 28] This figure shows another example of an optical fiber. [Figure 29] This flowchart illustrates how to perform absolute measurements of a system under test according to several embodiments. [Figure 30] In some embodiments, this is a block diagram of a circuit that may be used to carry out various functions, operations, activities, processes, and / or methods disclosed herein. [Modes for carrying out the invention]

[0007] The following detailed description refers to the accompanying drawings, which illustrate specific examples of embodiments in which the Disclosure may be put into practice, forming part of the Disclosure. These embodiments are described in sufficient detail to enable those skilled in the art to put the Disclosure into practice. However, other embodiments made available herein may be utilized, and modifications of structure, materials, and processes may be made without departing from the scope of the Disclosure.

[0008] The illustrations presented herein are not intended to be actual diagrams of any particular method, system, device, or structure, but are merely idealized representations employed to illustrate embodiments of the present disclosure. In some cases, similar structures or components in various drawings may retain the same or similar numbering for the convenience of the reader, but similarity in numbering does not necessarily mean that the structures or components are identical in terms of size, composition, configuration, or any other characteristics.

[0009] The following description may include examples that will help enable those skilled in the art to carry out the disclosed embodiments. The use of the terms “exemplary,” “as an example,” and “for example” means that the description relating to them is illustrative, and the scope of this disclosure is intended to include examples and legal equivalents, but the use of such terms is not intended to limit the embodiments or the scope of this disclosure to any specified components, steps, features, functions, or similar.

[0010] It will be readily apparent that components of embodiments generally described herein and illustrated in the drawings can be arranged, configured, and designed in a wide range of different configurations. Therefore, the following descriptions of various embodiments are not intended to limit the scope of this disclosure, but merely represent a variety of embodiments. Various aspects of the embodiments may be presented in the drawings, which are not necessarily drawn to scale unless otherwise noted.

[0011] Furthermore, the specific implementations illustrated and described are merely examples and should not be construed as the only way to implement this disclosure unless otherwise specified herein. Elements, circuits, and functions may be shown in the form of block diagrams to avoid unnecessarily detailing and obscuring this disclosure. Conversely, the specific implementations illustrated and described are merely examples and should not be construed as the only way to implement this disclosure unless otherwise specified herein. In addition, block definitions and the division of logic between various blocks are illustrative examples of specific implementations. Those skilled in the art will readily understand that this disclosure can be implemented by numerous other division solutions. In most cases, details regarding timing considerations and similar matters are omitted, as such details are not necessary for a full understanding of this disclosure and are within the scope of the skills of those skilled in the art.

[0012] Those skilled in the art will understand that information and signals can be represented using any of a variety of different techniques and methods. Some drawings may illustrate signals as single signals for clarity of presentation and explanation. A signal represents a signal bus, and buses have various bit widths, and those skilled in the art will understand that this disclosure can be carried out with respect to any number of data signals, including a single data signal.

[0013] The various exemplary logic blocks, modules, and circuits described in relation to the embodiments disclosed herein may be implemented or run on general-purpose processors, dedicated processors, digital signal processors (DSPs), integrated circuits (ICs), application-specific integrated circuits (ASICs), graphics processing units (GPUs), field-programmable gate arrays (FPGAs) or other programmable logic devices, discrete gates or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. The general-purpose processor (which may be referred herein as a host processor or simply a host) may be a microprocessor, but in alternative embodiments, the processor may be any conventional processor, controller, microcontroller, or state machine. The processor may also be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, multiple microprocessors, one or more microprocessors working with a DSP core, or any other such configuration. A general-purpose computer including a processor is considered a dedicated computer, but the general-purpose computer is configured to execute computing instructions (e.g., software code) relating to the embodiments of this disclosure.

[0014] These embodiments may be described in relation to processes represented as flowcharts, flow diagrams, structural diagrams, or block diagrams. Although flowcharts may describe operational activities as sequential processes, many of these activities may be executed in a different order, concurrently, or substantially simultaneously. In addition, the order of activities may be rearranged. Processes may correspond to methods, threads, functions, procedures, subroutines, subprograms, other structures, or combinations thereof. Furthermore, the methods disclosed herein may be implemented in hardware, software, or both. If implemented in software, these functions may be stored or transmitted as one or more instructions or codes on a computer-readable medium. Computer-readable mediums include both computer storage media and communication media, including any medium that facilitates the transfer of computer programs from one location to another.

[0015] In this specification, the use of designations such as “first,” “second,” etc., to refer to elements does not limit the quantity or order of those elements unless such restrictions are explicitly stated. Rather, these designations may be used herein as a convenient way to distinguish between two or more elements or between instances of elements. Therefore, references to first and second elements do not mean that only two elements may be used there, or that the first element must in some way come before the second element. In addition, unless otherwise noted, a set of elements may contain one or more elements.

[0016] As used herein, the phrase “substantially” with respect to a given parameter, characteristic, or condition means, and includes, the degree to which a person skilled in the art would understand that the given parameter, characteristic, or condition is met with a small degree of variation, such as within acceptable manufacturing tolerances. For example, depending on the specific parameter, characteristic, or condition that is substantially met, the parameter, characteristic, or condition may be met at least 90%, at least 95%, or even at least 99%.

[0017] As used herein, the term “continuous-wave electromagnetic (EM) radiation” refers to electromagnetic (EM) radiation that includes continuous waves, as opposed to pulsed-based electromagnetic (EM) radiation. Continuous-wave EM radiation may be at least substantially sinusoidal or modulated (e.g., amplitude modulation, phase modulation, or both). Continuous-wave EM radiation may mean that it is continuous over a given sample period in which a new series of measurements are taken along a desired optical time-of-flight delay range of the system under test. In pulsed OTDR or OFDR systems, EM radiation may be emitted for as little as 0.1% or less of the sample period, while continuous-wave EM radiation may be emitted for, for example, 50% or more of the sample period.

[0018] Pulse-based EM emission can be used for optical sensing. Since EM emission is active only during pulses and inactive between pulses, relatively few photons may be supplied to the optical system. Consequently, a relatively small number of photons are also received by the detector. Because the detector receives relatively few photons, a relatively low signal-to-noise ratio (SNR) of the reflected EM emission received by the detector can be expected in pulse-based EM synchrotron radiation sensing. Also, relatively short transmission distances (e.g., relatively short sensing fibers) can be made usable using pulse-based EM synchrotron radiation sensing. In addition, the use of amplifiers (e.g., semiconductor optical amplifiers (SOAs), erbium-doped fiber amplifiers (EDFAs), Raman amplifiers) may be required to amplify the reflected EM emission, which is low on average. As a result, increased cost, increased noise penalty, or both can be expected in optical sensing using pulse-based EM emission.

[0019] In pulse-based optical frequency-domain reflectance measurements (OFDR), the sample rate is tied to a single optical frequency sweep. Increasing the sweep speed improves the sample rate but requires a higher demodulation bandwidth. In pulse-based optical time-domain reflectance measurements (OTDR), the sample rate is limited by the overall time of flight traversing the sensor network under test, because a pulse train must be generated from a single pulse.

[0020] In pulse-based OFDRs (including time-gated OFDRs), the measured SNR is limited to approximately 1 microstrain (με) or several hundred nanostrains (nε) for strain measurements, or about one-tenth of a degree Celsius (°C). Transients are averaged over the required pseudolinear optical frequency sweep and typically returned as a single value. Pulse-based OTDRs appear to have the same SNR limitations as pulse-based OFDRs, but with the associated strain limitations.

[0021] In OFDR, for a given frequency spectrum, efficient spectral utilization requires that the sensors (or reflective features) of interest be equally spaced (e.g., equally spaced along the fiber or space under test) so that the sensors (or reflective features) occupy a high percentage of the OFDR frequency spectrum at equal intervals. If the sensors (or features) cover a subset of the spectrum or portions at irregular intervals, it may be difficult to efficiently demodulate the sensors (or features).

[0022] Pulse-based OTDR and OFDR technologies can require relatively expensive, specialized components, which drives up the overall manufacturing cost of pulse-based OTDR and OFDR systems.

[0023] As a concrete example of optical sensing using pulse-based EM radiation, a 50-kilometer (km) optical time-domain reflectometer (OTDR) system with a spatial resolution of 1 meter (m) could be used. Assuming an EM radiation pulse with a pulse width of 10 nanoseconds (ns), the pulse repetition rate is the dual-path optical time-of-flight delay (effectively (10 ns / m) × (50 × 10)). 3 This is effectively limited to 0.5 milliseconds (ms) due to m). Assuming a peak pulse power of Ppk, the average power Pave is less than or equal to Ppk × 10 ns / 0.5 ms, i.e., Pave ≤ 2 × 10 -5 Although various techniques can be used to widen the pulse width while maintaining spatial resolution, the average power Pave can only increase by a practical order of magnitude. As a result, the average power Pave can still be reduced to practically 1 / 10,000 of the peak pulse power Ppk.

[0024] Disclosed herein is an optical sensing system that uses continuous-wave EM radiation. EM radiation can be supplied to the optical system continuously, rather than using pulsed-based EM radiation. As a result, with respect to a given EM radiation source output, significantly more EM radiation is supplied to the optical system with continuous-wave EM radiation compared with pulsed-based EM radiation.

[0025] One example of using continuous-wave EM emission is OCoDR (Optical Code-Delay Reflectometry), which can be used as a continuous-wave technique. Measurements are available relatively quickly and continuously, up to several orders of magnitude faster than OFDR techniques. As a result, OCoDR can benefit from superior sample rates compared to OFDR.

[0026] OCoDRs can use continuous-wave EM radiation sources and thus continuously capture data from all sensors (or reflective features) in the system under test. Compared to OTDRs, OCoDRs can enable the capture of more photons per unit time and therefore have a better SNR for measurements at a given sample rate. Compared to OTDRs and OFDRs, there is no loss of temporal data (for example, between OTDR pulses, or within OFDR sweep pulses, between OFDRs, where the sweep may be a pulse in which the output is injected into the fiber under test while sweeping, and then the output is turned off or the data is ignored). Instead, the data can be considered as a continuous, uninterrupted entity in time.

[0027] In OCoDR, the spectral response of the system under test can "slide" across a pseudo-(or somewhat fixed-wavelength) light source. Therefore, the dynamic range of OCoDR is not limited by the wavelength sweep range, as in OFDR.

[0028] The costs associated with OCoDRs can also generally be lower than those associated with OFDRs and OTDRs. Relatively inexpensive components, and even lower-cost sensing fibers, may be used. In non-limiting examples, one or more Rayleigh scattering phenomena and / or Raman scattering phenomena may be used to perform sensing using standard telecommunications fibers or other fibers that do not incorporate conventional optical sensors (e.g., fiber Bragg gratings).

[0029] In OCoDR, the required spectral bandwidth can be tuned to the desired number of sensors (or features) within the fiber (or space) under test. In addition, OCoDR offers selectivity that can be modified on the fly. Therefore, OCoDR may offer superior spectrum utilization compared to OFDR and OTDR.

[0030] Since OCoDR is an interferometric measurement technique, the SNR is improved compared to non-interferometric measurement techniques (such as some OTDR techniques). The amplitude of the light field is encoded into the signal intensity within the photodetector and / or signal processing unit.

[0031] OCoDRs can also have superior detection ranges compared to OFDRs, which can be limited to tens or hundreds of meters. OCoDRs, like OTDR technology, can achieve sensing lengths of several kilometers or tens of kilometers. A 50km optical system can be used as a concrete example of optical sensing using continuous wave EM radiation. Because continuous wave EM radiation is used, the average power Pave is equal to the peak power Ppk. As a result, several orders of magnitude more EM radiation is available for interrogation and acquisition compared to optical sensing using pulse-based EM radiation. The more EM radiation there is, the better the SNR, the longer the range, or both.

[0032] OCoDR can also yield a complex polarization diversity optical field. Used in combination with orthogonal and polarization diversity modulation / reception, OCoDR can recover a complete complex optical field, including the polarization state at each sensor (or feature or location) along the system under test, distinguished by the polarization transmission state. Therefore, OCoDR can be used to measure the birefringence of a fiber, which can then be used, without limitation, to measure axial loads and other phenomena.

[0033] Figure 1 is a block diagram of the measurement system 100 in several embodiments. The OCoDR utilizes one or more unique code sequences to intergate to the optical system 116 under test. The system under test 116 may include multiple sensors (or, for example, features, layers, or segments). The measurement system 100 comprises an EM radiation source 102, an optical splitter 118, a modulator 112, a modulation signal source 114, an optical circulator 120, the system under test 116, a receiver 140, and a control circuit 104. The EM radiation source 102 is configured to supply continuous wave EM radiation 122 at a substantially fixed optical frequency (i.e., fixed wavelength). In a non-limiting example, the EM radiation source 102 may be a fixed-frequency laser. There are advantages to using a narrow-linewidth laser such as one with a narrow optical phase noise bandwidth.

[0034] The optical splitter 118 includes a splitter input 132, a first splitter output 134, and a second splitter output 136. The splitter input 132 is configured to receive continuous wave EM radiation 122 from the EM radiation source 102. The optical splitter 118 is configured to send the continuous wave EM radiation as incident EM radiation 124 to the first splitter output 134 and as reference EM radiation 130 to the second splitter output 136.

[0035] A modulation signal source 114 supplies a modulation signal 138 (one or more electrical signals) to a modulator 112 to modulate the incident EM radiation 124. The modulator 112 is configured to receive the incident EM radiation 124 from a first splitter output 134. The modulator 112 is configured to provide a sequence of amplitude, phase, or both of these to the incident EM radiation 124 in response to the modulation signal 138 from the modulation signal source 114 to generate modulated EM radiation 126. As an unrestricted example, the modulator 112 may use real pattern modulation (e.g., two-phase shift modulation (BPSK)) or complex pattern modulation (e.g., four-phase shift modulation (QPSK)). Also as an unrestricted example, the modulator 112 may provide a real or complex sequence to the single-polarization component or the double (e.g., orthogonal)-polarization component of the incident EM radiation 124. The modulated EM radiation 126 includes continuous-wave EM radiation. As a non-limiting example, the phase of the incident EM radiation 124 can be modulated with a simple phase modulator. Also, as a non-limiting example, the incident EM radiation 124 can be modulated with a real or complex (e.g., Mach-Zehnder) modulator.

[0036] The optical circulator 120 is configured to transfer the modulated EM radiation 126 from the modulator 112 to the system under test 116 and the reflected EM radiation 128 from the system under test 116 to the receiver 140 (the second input 146 of the receiver 140). In some embodiments, instead of using the optical circulator 120, a splitter, or a splitter and isolator, may be used to transfer the modulated EM radiation 126 to the system under test 116 and the reflected EM radiation 128 to the receiver 140.

[0037] Figure 1 illustrates an optical coupler used as a splitter and / or combiner (e.g., optical splitter 118, optical circulator 120), but it can be used in other devices. Non-limiting exemplary embodiments of the splitter include optical fiber couplers, free-space beam splitters, photonic integrated circuit (PIC) waveguide splitters, or other splitters. Non-limiting exemplary embodiments of the combiner include optical fiber couplers, free-space beam splitters, photonic integrated circuit (PIC) waveguide combiners, or other combiners. Another non-limiting exemplary embodiment of the optical splitter 118 may be a free-space or optical fiber circulator. In addition, other components such as polarizing beam splitters, isolators, or other components may be used to improve signal power or other aspects of the measurement system 100.

[0038] In some embodiments, the system under test 116 may include an optical fiber. The optical fiber exhibits Rayleigh backscatter due to irregular variations in core ellipticity, concentricity, dopant concentration, and other properties. These irregular variations, resulting from defects in the manufacture of the optical fiber, may have detectable traces for measuring mechanical stress or thermal effects acting on the optical fiber. In some embodiments, the optical fiber may include a fiber Bragg grating (FBG) sensor, a partial reflector, or other sensor. In some embodiments, the system under test 116 may be a free-space optical element (e.g., a free-space environment or space under test, which may or may not include air). As a non-limiting example, modulated EM radiation 126 may be interfaced to a free-space optical element using a system such as a lens, other light guide device, etc., so that three-dimensional space is scanned.

[0039] Fiber Bragg gratings can be used as sensors, but in some embodiments they may have the drawback that the return loss is a strong function of wavelength, and therefore the SNR may be poor if the desired sensor shows a weak response at wavelength λ0 and an undesired sensor shows a strong response at the same wavelength for a given set of environmental conditions acting on the system under test 116. Chirp fiber Bragg gratings show a relatively constant return loss over their wavelength response and are therefore not plagued by this drawback. Fiber Bragg gratings that show a broadband response (with respect to the desired system dynamic range) may also improve performance in terms of this drawback. Standard telecommunications fibers exhibit small variations in ellipticity and core concentricity, resulting in a level of Rayleigh scattering sufficient to perform sensing according to this disclosure. The random scattering centers of the optical fiber can be modeled as fiber Bragg gratings with random refractive index variations, providing similar advantages to the system under test 116, which includes numerous broadband fiber Bragg gratings. The advantage of using standard telecommunications fibers in conjunction with OCoDR via Rayleigh scattering analysis is that the cost of the sensor fiber is dramatically reduced.

[0040] The receiver 140 includes one or more optical hybrids 110 (e.g., 90-degree hybrids) and a plurality of photodetectors (photodetector 106, photodetector 108). In a non-limiting example, the receiver 140 may be configured with a polarization splitter and filter (e.g., a polarization beam splitter) and two optical hybrids that generate two signals for each orthogonal polarization state. In some embodiments, the receiver 140 does not use optical hybrids (e.g., a single coupler may be used rather than an optical hybrid 110 as illustrated in Figure 15). In such embodiments, a single coupler may be used to interface the output to a single photodetector. Such modulation schemes may be single-sideband or complex modulation may be utilized. The receiver 140 is configured to receive a reference EM emission 130 from a second splitter output 136, receive reflected EM emission 128 from the system under test 116 in response to the modulated EM emission 126, and generate an interference EM emission 142 in response to the reference EM emission 130 and the reflected EM emission 128.

[0041] Each optical hybrid 110 includes a first input 144 (sometimes referred to as the “local oscillator” input), a second input 146, a first output 148, and a second output 150. Each optical hybrid 110 receives two optical fields as inputs (i.e., reference EM radiation 130 and reflected EM radiation 128). The first hybrid input 144 receives the reference EM radiation 130, and the second input 146 receives the reflected EM radiation 128. Each optical hybrid 110 splits the reference EM radiation 130 and the reflected EM radiation 128, delaying one of them by substantially 1 / 4 wave (λ / 4) at the nominal wavelength λ with respect to the other. The optical hybrid 110 interferes the reference EM radiation 130 and the reflected EM radiation 128 to generate an interfered EM radiation 142.

[0042] The interferometric EM radiation 142 includes a common-mode interferometric output 152 supplied by the first hybrid output 148 and a quadrature interferometric output 154 supplied by the second hybrid output 150. In some embodiments, the optical hybrid 110 may supply two outputs for common-mode and two other outputs for quadrature. The intensities of the common-mode interferometric output 152 and the quadrature interferometric output 154 may be proportional to the amplitude of the beat signal formed by the interference between the reference EM radiation 130 and the reflected EM radiation 128.

[0043] The photodetector 106 is configured to convert the common-mode interference measurement output 152 into a first measurement signal 156 and to supply the first measurement signal 156 to the control circuit 104. Similarly, the photodetector 108 is configured to convert the quadrature-phase interference measurement output 154 into a second measurement signal 158 and to supply the second measurement signal 158 to the control circuit 104. The photodetectors 106 and 108 may include photodiodes. In a non-limiting example, in an embodiment in which the optical hybrid 110 includes two outputs for common-mode and two other outputs for quadrature, the photodetectors 106 and 108 may pair the two common-mode outputs and subtract the photodiode current of one from the photodiode current of the other. The same may be done for the two quadrature-phase outputs.

[0044] The control circuit 104 is configured to receive a first measurement signal 156 and a second measurement signal 158, interpret the first measurement signal 156 and the second measurement signal 158, and apply appropriate signal processing to uniquely extract information from each sensor, feature, layer, and / or segment of the system 116 under test. In some embodiments, the control circuit 104 includes a modulation signal source 114 that can thus generate a modulation signal 138 and supply the modulation signal 138 to a modulator 112. In some embodiments, the control circuit 104 includes a transimpedance amplifier which may be used at the input of the control circuit 104 to convert the current supplied by the photodetectors 106 and 108 into potentials. In some embodiments, the control circuit 104 includes a waveform acquisition unit (e.g., analog signal conditioning electronics, analog-to-digital converter) for sampling the potentials.

[0045] The control circuit 104 is also configured to process a continuous interferogram that may be generated in the coupling coupler of the optical hybrid 110 in response to the interference EM radiation 142 represented by the first measurement signal 156 and the second measurement signal 158. In some embodiments, the control circuit 104 includes a controller (for example, a processing unit such as a central processing unit (CPU), a field-programmable gate array (FPGA), a graphics processing unit (GPU), a system-on-a-chip (SoC), other processing units, or a combination thereof).

[0046] During operation, the EM radiation source 102 supplies continuous-wave EM radiation 122 at a substantially fixed optical frequency (wavelength). The optical splitter 118 splits the continuous-wave EM radiation 122 and supplies it to the modulator 112 and the first hybrid input 144 (e.g., the local oscillator input) of the receiver 140 of the (optical hybrid 110). If there is no modulator 112, for the sake of discussion only, assuming that the system 116 under test is a fiber under test having only one non-negligible reflection (e.g., a mirror), the EM radiation is incident on the fiber under test, and the EM radiation is reflected from the mirror (reflected EM radiation 128). The reflected EM radiation 128 is subject to interference with the reference EM radiation 130.

[0047] The optical field is a complex phasor u(t)=ρ(t)e iφ(t) and can be represented by. The losses α l , α d in the local oscillator and system-under-test paths are assumed respectively, and these optical fields at the receiver are

[0048]

Number

[0049]

Number

[0050] can be written as, where ρ(t) is the amplitude of the optical field, and τ l and τ d are the optical flight-time delays through the local oscillator path and the system-under-test path respectively.

[0051] The two fields (u l (t) and u d(t)) is interfered with in receiver 140 (complex receiver), generating an interferogram at the output of optical hybrid 110. In receiver 140, a matching detector is often used, where the common-mode current is subtracted. The resulting interference measurement electrical signal can be digitized via the waveform acquisition unit of control circuit 104. The common-mode signal and the quadrature signal can be assigned to the real and complex parts of the complex number, respectively. The resulting signal is, U cplx (t) ∝ α l α d ρ(t-τ l )ρ(t-τ d )e iθ(t) It is often given by, here, θ(t)=φ(t-τ l )-φ(t-τ d ) Therefore, if the continuous wave EM radiation 122 has a fixed optical frequency, the frequency and phase expansion is: v(t)=v0 φ(t)=2π∫v(t)dt=2πv0t It may be given by, where v0 is the nominal fixed optical frequency of the continuous wave EM emission 122. In this case, θ(t)=2πv0Δτ And here, Δτ = τ d -τ l That is the case.

[0052] Therefore, signal U cplx (t) is the loss (α) through the system under test. dThis is a phasor having a magnitude proportional to Δτ and a phase proportional to the optical time-of-flight difference between the local oscillator path and the system under test path. This phase traverses 2π radians when Δτ changes by an amount of 1 / v0. Considering the example of v0 = 193.4 terahertz (THz) (wavelength 1550 nanometers (nm)), the optical path length required for the phasor to oscillate completely is substantially 5.2 femtoseconds (fs). Assuming that the dual-path optical path length of a typical optical fiber is substantially 10 ns per meter, the optical path length for one oscillation of the interferometric phasor is substantially a physical path length change of 0.5 μm in the optical fiber. Furthermore, if the complex plane (in which the phasor is placed) can be digitized with multi-bit precision, an equivalent physical path length change of 1 nm or more can be obtained by analyzing the interferometric phasor.

[0053] In this example, we considered the case where only one non-negligible element in the system under test reflects the incident light field. In a dispersed optical sensing scenario, the system under test could contain a large number of sensors (tens, hundreds, thousands, tens of thousands, or more) written along the fiber, all of which can be uniquely demodulated (i.e., interrogated). Alternatively, or in addition, the optical fiber could be any optical fiber exhibiting Rayleigh backscatter distributed along the fiber, which is due to random defects in the optical fiber (e.g., as a result of an imperfect manufacturing process).

[0054] As previously mentioned, the modulator 112 is used to give the incident EM radiation 124 a real modulation pattern or a complex modulation pattern, generating modulated EM radiation 126 that allows multiple sensors or arrangements to be uniquely demodulated.

[0055] In some embodiments, the modulation signal 138 supplied to the light via the optical modulator 112 is a pseudo-random binary sequence (PRBS). In such embodiments, the optical phasor of the continuous wave EM radiation 122 emanating from the EM radiation source 102 (and on the incident EM radiation 124 supplied to the modulator 112) is substantially multiplied by either +1 or -1. As a non-limiting example, e i0 =1 and e iπ Since = -1, this multiplication by +1 and -1 can be achieved by a phase modulator that moves the incident light field through either π / 2 radians or -π / 2 radians (or actually any two angles separated by π radians). In this case, the amplitude of the light field exiting the modulator does not change. The phasor can be rotated around the unit circle depending on the binary number of the PRBS employed.

[0056] Furthermore, as a non-restrictive example, multiplication by +1 and -1 may be performed using a Mach-Zehnder interferometer. In such embodiments, the phasor of the incident EM radiation 124 can be moved to a point π radians away from the nominal zero-radian state by moving the phasor through the origin of the unit circle. Commercial optical modulators often have a Mach-Zehnder interferometer implemented within the modulator and can be used for this purpose as modulator 112. Modulation using a Mach-Zehnder interferometer is similar to BPSK optical modulation, and a real modulator would suffice for this purpose. Complex modulators can also be used to impart a BPSK constellation to the incident optical field.

[0057] In some embodiments, PRBS for the modulated signal 138 may be generated via a linear feedback shift register (LFSR) of a high-efficiency digital processor (e.g., CPU, FPGA, GPU, SoC, etc.). If the LFSR consists of M bits, the PRBS of maximum length or m sequences can be up to 2 MIt can be generated at -1. This maximum length PRBS can be fed to the incident EM radiation 124 via the modulator 112 and injected into the system under test 116 (e.g., the fiber under test) as modulated EM radiation 126. As used herein, the term “tip time” refers to the time required for one sample (i.e., tip) of the PRBS to progress to subsequent samples. As used herein, the term “sequence time” refers to the entire sequence of the modulated signal 138 (in this non-limiting example, 2 M This refers to the time required to modulate (-1) units.

[0058] It may be useful to illustrate the application of PRBS to system 116 under test, which has one reflector. The binary signal is then used to produce the desired zero-radian or π-radian shift.

[0059]

number

[0060] It is often defined as such, where A(t) is a PRBS having values ​​in the set {-1, +1}. This is V π This can be achieved by driving a phase modulator with two signals having different potential values, where V π This is the potential that, when applied to the modulator 112 (for example, an optical phase modulator), results in a phase shift of π radians.

[0061] If the light source power ρ(t) changes slowly compared to the sequence time, the interference measurement signal is:

[0062]

number

[0063] It may be given by U cplx(t) is digitized (for example, using a waveform acquisition unit), U cplx (t) is a pseudo-random binary sequence A(t-τ) d When multiplied by ),

[0064]

number

[0065] This can be calculated. Since (t) can only take two values ​​(+1 and -1),

[0066]

number

[0067] It becomes 1, that is,

[0068]

number

[0069]

number

[0070] Please note that this is the case. Therefore, when the interferogram is multiplied by PRBS, the signal becomes the desired phasor.

[0071]

number

[0072] It will be restored.

[0073] PRBS exhibits a useful autocorrelation property in that its autocorrelation function is 1 when the shift is zero, but for any other shift value where N is the sequence length, it shows a small value of -1 / N. In other words, when PRBS is multiplied by the same PRBS with a zero shift, -1 values ​​are multiplied by -1 values, +1 values ​​are multiplied by +1, and the signals are perfectly correlated. When these values ​​are summed over one sequence time, the result is N. For any other shift, the result of multiplying PRBS and a cyclic shift is 2, where the product is +1. M-1 The result of multiplication is -1, and the product is -1. M-1 The result is [number]. When these values ​​are summed up over one sequence of time, the result is -1.

[0074] For zero-shifted and non-zero-shifted data, these correlation values, when normalized by N, can yield a correlation of 1 for zero-shifted data and a correlation of -1 / N for non-zero-shifted data. As a result,

[0075]

number

[0076] And here, t c This is the tip time, and t c = 1 / f s and f s is the sample rate of the PRBS. As the sequence length N increases, the value of the autocorrelation function for non-zero shifts decreases.

[0077] If the m-sequence of PRBS is continuously repeated over time, a cyclic shift (e.g., "circshift") may not be necessary. A standard shift of one signal with respect to another signal, where the single sequence time of the longer signal considered in the summation is the primary signal, will yield similar results.

[0078] Having described the case of a single reflector, the case of multiple reflectors will now be illustrated. It is assumed that the system under test 116 (e.g., the fiber under test) includes n reflectors (e.g., multiple reflectors, FBGs, Rayleigh scattering configurations, or a combination thereof). It is also assumed that a phase modulator is used to supply the modulated EM radiation 126 to the system under test 116 by providing a PRBS signal (modulated signal 138) to the incident EM radiation 124. Each reflection from the system under test 116 is at a unique position τ j This occurs at j=1, ..., n. The n back reflections are superimposed,

[0079]

number

[0080] It forms a fixed-frequency continuous wave EM radiation 122, and this field interferes.

[0081]

number

[0082] It forms an additional term,

[0083]

number

[0084] The additional items are:

[0085]

number

[0086] The system has components in the , where p is the index of the additional sum over the fiber under test term. The local oscillator field is considerably stronger (i.e., α) than the reflected system field under test. l ≫α dIn this case, the contribution of these additional terms to the overall interferogram is negligibly small. The control circuit 104 (for example, the processing unit of the control circuit 104) cplx (t) is digitized, multiplied by a pseudo-random sequence, and then summed over the sequence time.

[0087]

number

[0088] It is often assumed that this forms a constant ρ(t) over sequence time.

[0089] Based on the correlation characteristics of PRBS described above,

[0090]

number

[0091] and

[0092]

number

[0093] As described above, as M increases, 1 / N decreases, and the influence of the second term also decreases. v0Δτ j Because it easily crosses 2π radians due to environmental perturbations, for a considerable number of reflectors n

[0094]

number

[0095] It can be assumed that these are distributed almost uniformly across the unit circle, which further collapses the second term of the previous equation, and as a result,

[0096]

number

[0097] Therefore, by multiplying the m-sequence PRBS by the composite interferogram and integrating the result over sequence time, the phasors can be recovered for any desired reflector in the system 116 under test. The desired elements in the system 116 under test can be tuned by appropriately delaying the PRBS by an amount equal to the optical time-of-flight delay to each element.

[0098] A pseudo-random binary sequence is just one example of a host of sequences that the modulation source 114 can use to supply the modulated signal 138 to the modulator 112. Any signal that exhibits substantially zero autocorrelation for any non-zero shift of the modulated signal 138 may also be used. In some embodiments, the modulation source 114 may use a family of signals known as constant amplitude, zero autocorrelation (CAZAC) signals, or even a zero autocorrelation zone (ZACZ) or region. A CAZAC sequence exhibits exactly zero autocorrelation for all non-zero shifts of the sequence. As a result, a CAZAC sequence used for the modulated signal 138 may perform better than a PRBS that has a small but non-zero autocorrelation for non-zero shifts. An example of a CAZAC sequence is the Zadoff-Chu sequence. A ZACZ signal has a region of continuous delay shifts in which the autocorrelation is substantially or exactly zero.

[0099] The procedure for applying one of these zero or small autocorrelation sequences to the modulated signal 138 is the same as that described above for PRBS. The real-valued or complex-valued zero autocorrelation (or small autocorrelation) sequence is given to a laser beam of substantially fixed frequency by combining the signal (real part or real and imaginary part) and driving a real modulator or complex modulator (modulator 112) with each signal (modulated signal 138). This sequence is injected into the system 116 under test via modulated EM radiation 126. The modulated EM radiation 126 imposes an inherent time-of-flight delay on the inherent reflector (whether FBG, Rayleigh scattering, other scattering mechanism, or other reflection mechanism). The reflected EM radiation 128 (modulated and variably delayed EM radiation) is interfered with substantially single-frequency EM radiation (reference EM radiation 130) to produce an interferogram 142 (i.e., interfering EM radiation). The interferometric emission 142 is converted into analog electrical signals (first measurement signal 156 and second measurement signal 158), which are then digitized to form a continuous digitized interferogram (for example, in the digital signal processor of the control circuit 104).

[0100] After the interferogram is sampled, either a time-domain or frequency-domain approach can be taken. In the time-domain approach, the interferogram is multiplied by a time-shifted complex conjugate version of its sequence. The time shift corresponds to the time-of-flight position of the system 116 under test. This product is integrated over one sequence time to form a phasor. The magnitude of the phasor is proportional to the reflectance at the position corresponding to the time-of-flight of light to the position along the system under test. The phase of the phasor changes proportionally to the time-of-flight position of the reflecting (or scattering) element.

[0101] In the frequency domain approach, the digitized interferogram and the signal with virtually zero autocorrelation can be Fourier transformed. The complex conjugate of the Fourier transform of either the original sequence (one period or sequence time of this signal) or one sequence time of the interferogram is taken. The inverse Fourier transform of the product of the two signals is then applied. The resulting signal is a vector of phasors. The magnitude of the phasors in the vector is proportional to the reflectance at the time-of-flight position along the system 116 under test. The phase of the phasors is proportional to the time-of-flight of light to the position along the system 116 under test.

[0102] Figure 2 is a signal processing diagram illustrating a multiplier-accumulator architecture 200 for performing OCoDR according to several embodiments. In operation 202, the multiplier-accumulator architecture 200 includes generating a sequence. As a non-limiting example, the multiplier-accumulator architecture 200 may be implemented by the control circuit 104 in Figure 1. The multiplier-accumulator architecture 200 may be used to uniquely demodulate elements in the system under test 116 in Figure 1 at a specific optical time-of-flight delay.

[0103] In operation 202, the multiplier-accumulator architecture 200 includes generating sequences (e.g., PRBS, zero autocorrelation sequence, substantially zero autocorrelation sequence, CAZAC sequence, Zadoff Chu sequence). The values ​​of the sequences may, by various embodiments, include real components, imaginary components, or both. The values ​​may be provided to the delay network 208 for later use when extracting separate phasors 218 from the first measurement signals 156 and the second measurement signals 158 received from photodetectors 106 and 108, respectively (Figure 1).

[0104] In operation 204, the multiplier-accumulator architecture 200 includes converting a continuous stream of complex numbers into a continuous (repeating) sequence into a real part 210 and an imaginary part 212. In operations 214 and 216, respectively, the multiplier-accumulator architecture 200 includes converting the real and imaginary parts of the sequence from their digital representations to their analog representations, for example, via a digital-to-analog converter. The real part 210 may be transmitted as the in-phase component of the modulated signal 138, and the imaginary part 212 may be transmitted as the quadrature component of the modulated signal 138. As described above, the modulated signal 138 is supplied to the modulator 112, which modulates the incident EM radiation 124 to produce the modulated EM radiation 126, which is supplied to the system under test 116 (Figure 1). In response, reflected EM radiation 128 is received from the system under test 116, interfered with by reference EM radiation 130, and the interfering EM radiation 142 is converted by photodetectors 106 and 108 to yield a first measurement signal 156 and a second measurement signal 158 (Figure 1). The first measurement signal 156 and the second measurement signal 158, each containing in-phase and quadrature components, are converted from analog representation to digital representation in operations 220 and 222, respectively, for example, via a digital-to-analog converter. In operation 206, the multiplier-accumulator architecture 200 includes converting the in-phase (e.g., real) and quadrature (e.g., imaginary) components of the continuous interferogram into a continuous stream of complex numbers. The complex number stream is then multiplied by the delayed conjugate value of the sequence (assuming a complex sequence, but real sequences do not use complex conjugates, or the complex conjugate of a real sequence is simply the same real sequence), and these values ​​are supplied in operation 202 (generating the sequence). For PRBS, the multiplier may simplify the operation mode input to the accumulator. The product of the complex number and the delayed conjugate value of the sequence is summed over the sequence time to generate a separate phasor 218 for each delay of the delay network 208.Alternatively, if the conjugate of the complex sequence is taken and sent to operation 204, the native value (i.e., the non-conjugate value) may be supplied to the delayed network 208.

[0105] PRBS can be applied to a composite signal by supplying a PRBS signal to the operating mode input of an accumulator, resetting the accumulator every N operating cycles, and taking a response in the operating cycle preceding the reset. The binary point of the response can then be left-shifted by M bits, and the response can be approximately divided by N.

[0106] Figure 3 is a signal processing diagram illustrating frequency domain architecture 300 for performing OCoDR according to several embodiments. For large n, the complexity in the digital signal processing implementation can be improved by applying a pseudo-random sequence in the frequency domain (e.g., the Fourier transform domain). This can be achieved by performing a Fourier transform of the pseudo-random sequence (e.g., saving the Fourier transform of the pseudo-random sequence by choice). For each sequence time, the interference measurement signal output from receiver 140 (Figure 1) is acquired, digitized, and a Fourier transform of the interferogram is performed, which may be multiplied by the Fourier transform of a zero (or substantially zero or small) autocorrelation sequence (either the Fourier transform of the sequence or the Fourier transform of the interferogram is complex conjugated), and the inverse Fourier transform of the result may be performed.

[0107] These operations can result in obtaining the vector of the phasors. Each phasor can result in the amplitude and phase of the element at its respective flight time delay along the system 116 (FIG. 1) (e.g., fiber) under test. A cyclic cross-correlation of the sequence (sequence) and the interferogram can be returned. Since the sequence (sequence) is a repeating signal having a repeating length equal to the sequence (sequence) length, a cyclic shift of a single repeating length of the sequence (sequence) is the same as a linear shift in the repeating sequence (sequence) stream. As a result, the cyclic cross-correlation yields the same result as applying the appropriately delayed sequence (sequence) to the interferogram individually. As a result, an algorithm with complexity ΩNlogN is obtained. If log2N < n, this can result in a more efficient implementation form.

[0108] When the phasors are recovered for each delay k = 0…N−1, the frequency domain architecture 300 is equal to the cyclic convolution of the sequence (sequence) and the interferogram. The cyclic convolution in the time domain can be implemented via multiplication in the frequency domain.

[0109] In some embodiments, instead of taking the complex conjugate of the sequence (sequence), the complex conjugate of the complex signal from the receiver may be taken.

[0110] FIG. 4 is a digital signal processing diagram illustrating a Zadoff-Chu sequence (sequence) architecture 400 for performing OCoDR according to some embodiments. A Zadoff-Chu sequence of any length to the rth root can be generated (e.g., by the modulation signal source 114 (FIG. 1)). The Zadoff-Chu sequence (sequence) can be transmitted (e.g., by the modulation signal source 114) to a modulator (e.g., the modulator 112 in FIG. 1) via a waveform synthesis subsystem. A complex signal (interferogram), which is a superposition of the modulated backscattered phasors, can be received (e.g., by the control circuit 104) from the system 116 (FIG. 1) (e.g., fiber) under test.

[0111] In some embodiments, the complex conjugate of either the sequence or the interferogram may be taken. In some embodiments, the complex conjugate of the sequence is sent to the waveform synthesis module, and the complex conjugate of the sequence and the interferogram may not be taken before the complex multiplication and Fourier transform. Complex multiplication of the sequence and the interferogram may be performed, and the Fourier transform of the product may be taken. The result is a phasor vector. Linearity in optical time-of-flight delay may be determined for one of the given phasor vectors. The magnitude of the phasor is proportional to its reflectance in optical time-of-flight along the system 116 under test. The phase of the phasor is proportional to the optical time-of-flight delay along the system 116 under test.

[0112] When signal processing is performed according to the Zadoff-Chu sequence architecture 400, a Fourier transform of the conjugate Zadoff-Chu sequence multiplied by the interferogram may be performed. The conjugate Zadoff-Chu multiplication sets up a Fourier series. The phase offset in this series may be taken into account when the phases of multiple samples of the Fourier series are analyzed.

[0113] The Zadoff-Chu sequence is

[0114]

number

[0115] It is often calculated as follows, where N is the sequence length and c f = mod(N,2), where q∈Z imposes a cyclic shift on zero-shifted (e.g., Zadoff-Chu) sequences, and r∈Z defines a sequence as an r-th root sequence.

[0116] t = 1 / f s When k=1, then k=tf sTherefore, the Zadoff-Chu sequence is obtained in continuous time.

[0117]

number

[0118] It can be expressed as follows. This Zadoff-Chu sequence is delayed by τ and multiplied by its conjugate z(t)

[0119]

number

[0120] This is possible, but when it is discretized...

[0121]

number

[0122] Therefore, the discrete-time index k can be incremented by 1.

[0123]

number

[0124] This can be significant because q acts as a shift to the Fourier series, just as it acted as a shift to the sequence. Term c f This value is either 0 (even sequence) or 1 (odd sequence), which represents a half-sample shift relative to the odd sequence length.

[0125] The phase increment per 2π sample is,

[0126]

number

[0127] or

[0128]

number

[0129] This can occur with a sample rate f. s If there are N samples in the Zadoff-Chu sequence, then there are N positions in the Fourier transform, and the spatial resolution in the delay region is 1 / f s This is the result. A sequence of first roots that is even and has no shifts (i.e., q=c f For (=0, r=1),

[0130]

number

[0131] Therefore, the phase increment for each index is the second term in this equation. τ for each sample is 1 / f s It is already confirmed that it will increase by one increment at a time. The local oscillator field is

[0132]

number

[0133] It can be given by. The modulated DUT field reflected (or scattered) from a single reflector (scattering center) of the system under test is:

[0134]

number

[0135] It is often assumed that the Zadoff-Chu sequence z(t)(z(t)=e (-iζ(t)) The (defined as) is supplied to the incident light 138 via the modulator 112, forming the modulated EM radiation 126.

[0136] The interferogram at 156 is: U re ( t,τ d )∝ρ(t-τ d )α d (τ d )cos(φ(t-τ l )-φ(t-τ d )-ζ(t-τ d )) Given, the interferogram at 158 ​​is, U im ( t,τ d )∝ρ(t-τ d )α d (τ d )sin(φ(t-τ l )-φ(t-τ d )-ζ(t-τ d )) It is given by.

[0137] Function U cplx teeth,

[0138]

number

[0139] It can be given as follows: Here, θ d ( t,τ d )=φ(t-τ l )-φ(t-τ d )-ζ(t-τ d ) That is the case.

[0140] Fixed-frequency lasers are phase φ(t)=2πν o t It is modeled as representing, θ d ( t,τ d ) = -2πν o τ l +2πν o τ d -ζ(t-τ d ) This could lead to...

[0141] Next, it is possible to apply the conjugated Zadoff Chu sequence to the interferogram.

[0142]

number

[0143] This will result. The laser output may be assumed to be constant over a sequence length such that ρ(t) = ρ.

[0144]

number

[0145] The above is the left τ l and the right side τ d Includes the following items. Desired phasor

[0146]

number

[0147] The phase locus is time-linear τ d Additional phasors proportional to

[0148]

number

[0149] It is multiplied by this. In the Fourier transform domain, this is the desired phasor

[0150]

number

[0151] Flight time delay τ dis equivalent to assigning to a frequency proportional thereto.

[0152] When the system under test includes a large number of reflectors (or scattering centers, etc.), each phaser

[0153]

Number

[0154] is multiplied by a complex exponential whose frequency is

[0155]

Number

[0156] is multiplied. Thus, the Fourier series at τ in z*(t)·U cplx (t,τ d ) is set up. Then, the Fourier transform is performed, and the vector of the phaser d . can be generated, where the index m ranges from 0 to N - 1. An alternative expression of α

[0157]

Number

[0158] is as follows. Thus, the Fourier transform is the amplitude α d (τ d ) at position m / rf

[0159]

Number

[0160] and the phaser s at d (τ d ), and

[0161]

Number

[0162] results in a vector. The overall result is scaled by the loss α through the local oscillator path l and phase offset by the phase through the local oscillator path proportional to the time-of-flight delay τ l of the local oscillator path.

[0163] The Fourier transform terms can be put on the same phase reference by multiplying the Fourier transform output by

[0164]

Number

[0165] and eliminating the final term, resulting in

[0166]

Number

[0167] being obtained.

[0168] Optionally, the Zadoff-Chu sequence architecture 400 can include phase correction of the vector of the phaser pair delay. As a non-limiting example, the phase correction can include multiplication by the final phase term in the above mathematical handling.

[0169] FIG. 5, FIG. 6, FIG. 7, FIG. 8, and FIG. 9 are plots illustrating an example of the application of the Zadoff Chu sequence.

[0170] FIG. 5 is a plot illustrating an example of the phase derivative 500 of a square root, zero-shift Zadoff-Chu digital sequence. This Zadoff Chu sequence starts from a zero phase derivative (i.e., zero frequency), proceeds through negative frequencies to the negative Nyquist (-π phase derivative), then wraps around to the positive Nyquist and linearly proceeds to zero frequency. This digital Zadoff Chu sequence follows the definition given above, i.e.,

[0171] [Number]

[0172] where c f = 0, r = 1, and q = 0. Other choices for N, c f , r, and q can also be selected. For example, when using the Zadoff Chu sequence for OCoDR, since the length region is mapped to frequency, for a given sample rate f s , N can be increased to increase the sensing length or N can be decreased to increase the output sample rate of the system (i.e., the repetition rate of the Fourier transform of the Zadoff-Chu sequence architecture 400).

[0173] FIG. 6 is a plot illustrating the reflectivity 600 of an example of the composite system under test. The composite system under test includes three reflection features (the first reflector 602, the second reflector 604, and the third reflector 606) having a reflectivity of about -35 dB out of substantially -75 dB level of scattering. The horizontal axis is drawn in sequence samples, and a non-limiting exemplary sequence length 4096 is illustrated. For example, if the sample rate of the digital Zadoff Chu sequence sent to the digital-to-analog converter and then to the modulator is f s = 200 MHz, each sequence sample is 1 / f sThis represents an optical time-of-flight delay of 5 ns, which roughly corresponds to 0.5 meters in a glass optical fiber. In the example in Figure 6, reflectors 602, 604, and 606 are shown at sequence sample positions 897, 2237, and 3779, corresponding to approximately 448.5, 1118.5, and 1889.5 meters, respectively, along the fiber under test. Other scattering events are depicted along the fiber with considerably lower reflectivity. s In the example of 200MHz, the selection of N=4096 results in an OCoDR system with an addressable sensing length of 2048 meters. If longer fibers are connected to the OCoDR system, the portion of the fiber exceeding 2048 meters wraps around zero meters and is aliased to the system's 2048-meter capability. In this case, N can be increased to accommodate the length of the fiber. N=4096, f s If =200MHz, then f s This results in an output sample rate of / N (for all N locations along the fiber under test), which in this example is effectively 48.8 kHz. Consequently, increasing N increases the sensing length but decreases the output sample rate, and decreasing N does the opposite.

[0174] Figure 7 is a plot illustrating the phase derivatives 700 of the reflectors (first reflector 602, second reflector 604, and third reflector 606) in Figure 6. The phase derivatives include the first phase derivative 702 corresponding to the first reflector 602, the second phase derivative 704 corresponding to the second reflector 604, and the third phase derivative 706 corresponding to the third reflector 606. The phase derivative 700 also includes the reference phase derivative 708 corresponding to zero delay.

[0175] The positions of the three exemplary reflectors 602, 604, and 606 at 448.5, 1118.5, and 1889.5 meters result in digital Zadoff Chu sequence delays of 897, 2237, and 3779 samples, respectively. These signals are plotted graphically in Figure 7, with the reference derivative 708 (i.e., the one transmitted to the modulator is also included for reference) corresponding to the original sequence of the modulated signal 138 shown by a solid black line. This plot extends across two sequence lengths to show how the first phase derivative 702, the second phase derivative 704, and the third phase derivative 706 are 897-, 2237-, and 3779-sample delayed copies of the reference phase derivative 708. Phase derivatives of other features with non-negligible reflectivity (i.e., corresponding to smaller reflectors compared to the three exemplary primary reflectors with much higher reflectivity) plotted in Figure 6 are not shown. It should be noted that this drawing assumes that the Zadoff Chu sequence of the modulated signal 138 was output before the sample indicated as zero in the figure, as if the delayed reflector had already supplied the modulated sequence before sample zero. Although Figure 7 shows only two sequence lengths of consecutive repeating Zadoff Chu sequences, it will be understood that the Zadoff Chu sequence is used to continuously modulate the incident radiation 124 (Figure 1) of substantially fixed frequency through repeating sequences without interruption.

[0176] Figure 8 is a plot of the phase derivative 800 (phase derivative 700 in Figure 7) of the reflector signal after multiplying the complex conjugate of the original Zadoff Chu sequence, also transmitted to the modulator, with the interferogram, before fully considering the frequency wrapping effect achieved by the Nyquist sampling theorem. Phase derivative 800 includes the first phase derivative 802, corresponding to the first phase derivative 702 in Figure 7; the second phase derivative 804, corresponding to the second phase derivative 704 in Figure 7; and the third phase derivative 806, corresponding to the third phase derivative 706 in Figure 7.

[0177] Multiplication of the complex conjugate and the original Zadoff Chu sequence has the effect of taking the vertical difference between the phase derivatives shown in Figure 7. For example, the difference between the first phase derivative 702 and the reference derivative 708 in Figure 7 is observed by the long dashed line (first derivative 802) in Figure 8, the difference between the second phase derivative 704 and the reference phase derivative 708 is observed by the dashed line (second derivative 804), and the difference between the third phase derivative 706 and the third reference derivative 708 is observed by the short dotted line (third reference derivative 806). In some temporal examples (sequence samples), the reflector trace in Figure 7 lies on the reference (solid line) trace. The corresponding time in Figure 8 may represent a positive constant phase derivative (i.e., a positive frequency). At other times, the reflector trace in Figure 7 is below the reference trace, and the corresponding sample number in Figure 8 may exhibit a negative constant frequency (i.e., the phase derivative).

[0178] Figure 9 is a plot showing the phase derivatives 900 (frequency) arising from three exemplary reflectors (the first reflector 602, the second reflector 604, and the third reflector 606 in Figure 6) after fully considering the frequency wrapping effect achieved by the Nyquist sampling theorem. The phase derivatives 900 include the first phase derivative 902 corresponding to the first reflector 602, the second phase derivative 904 corresponding to the second reflector 604, and the third phase derivative 906 corresponding to the third reflector 606.

[0179] Positive Nyquist frequency f nyq This corresponds to the phase derivative of π radians, and is the negative Nyquist -f nyqThis corresponds to -π radians. When conjugation and multiplication are performed in the Zadoff-Chu sequence architecture 400, each reflector may be encoded by one of two phase derivatives (frequencies) at different times in sequence time, one phase derivative in the range of -π to +π radians and the other outside the range of -π to +π radians. Correct selection of digital sampling or resampling before multiplication with the conjugate sequence allows the resulting frequency components outside the range of -π to +π radians to alias within the range of -π to +π radians after multiplication with the sequence. This aliasing behavior can be visualized by "wrapping" the -π to +π radian range from Figure 7 into a conceptual "tube" such that -π radians coincide with +π radians. If wrapping continues in the same -π to +π range to other ranges (-3π to -π and +π to +3π), a given frequency outside the -π to +π range emanating from a given reflector will alias to the same frequency emanating from a reflector that was in the -π to +π range at other times.

[0180] As a result, the signal is digitized via an analog-to-digital converter at a sample rate corresponding to the sequence bandwidth (or the signal is resampled by lowering the originally higher sample rate to that sample rate corresponding to the sequence bandwidth), and after applying the conjugate sequence, all frequencies outside the range of -π to +π are aliased to corresponding frequencies within the range of -π to +π, as shown in Figure 9, and each position in the system under test corresponds to a single frequency for all time in the resulting signal. A Fourier transform is then performed (as shown in the Zadoff-Chu sequence architecture 400) to recover phasors for each position along the system under test that encode the reflectance of a given reflector (or scattering center, or sensor, etc.) and the time of flight of light to the given reflector. The magnitude trace of the Fourier transform in this example would look like Figure 6.

[0181] A Zadoff Chu sequence of any length N may be selected. A Fourier transform of length N may also be selected, but any length can be used. Furthermore, there are no requirements regarding the start or end position of the data being Fourier transformed (with respect to the Zadoff Chu sequence applied). In fact, this disclosure allows for setting up a time-continuous Fourier series, and, in contrast to OTDR or OFDR techniques where pulses or individual sweeps may be used, the system under test is illuminated and interrogated continuously without interruption. As a result, for a given laser output, more photons are injected into the system under test, more photons are reflected from the system under test and integrated into the receiver's photodetector, resulting in advantages such as enhanced SNR, extended sensing length, and / or improved output sample rate, among others. The Fourier transform length may be selected to trade off the sample rate with respect to spatial resolution. For example, selecting a Fourier transform length shorter than the sequence length results in a system sample rate faster than the reciprocal of the optical time-of-flight delay to the furthest point along the system under test, but compromises spatial resolution with respect to the maximum spatial resolution corresponding to the reciprocal of the sequence bandwidth.

[0182] The above treatment assumes baseband sequence modulation and reception, in that the local oscillator light is modulated by an electronic modulator input signal having a bandwidth substantially centered at DC (i.e., 0 Hz). When this signal is reflected from the system under test and interfered with by the local oscillator light, the resulting electronic interferogram exhibits a bandwidth substantially centered at DC (i.e., the baseband). A complex receiver incorporating an optical hybrid may be used to interfere the reflected light from the system under test with the in-phase and perpendicular-phase local oscillator light, forming a complex interferogram from which phasors for each position along the system under test can be inferred.

[0183] This sequence does not need to be centered on DC. This sequence can be mixed away from DC using either a real sine wave or a complex sine wave. Some embodiments include scenarios where the sequence is mixed away from DC using a real modulator. In such embodiments, two bandwidths may arise from a real mixed sine wave, as described with reference to Figure 12, and a sine wave amplitude envelope may be used to indicate the orientation of the signal, but not to represent the spectral components of the various sequences that can be used.

[0184] Figure 10 is a diagram of one representation of a simple phase modulator 1000 according to several embodiments. The simple phase modulator 1000 is an example of modulator 112 in Figure 1. The simple phase modulator 1000 is configured to receive light 1002 from a local oscillator and to supply modulated light 1004 in response to the light from the local oscillator. The simple phase modulator 1000 includes a waveguide 1006 which is operated (e.g., via a tunable electric field) to generate a tunable optical time-of-flight delay. In a non-limiting example, the electronically driven waveform affecting the tunable optical time-of-flight delay may be created by a digital processor, synthesized via a digital-to-analog converter, and tuned by analog electronics before being supplied to the simple phase modulator 1000.

[0185] Figure 11 is a diagram of one representation of a real modulator 1100 (for example, a Mach-Zehnder modulator, but not limited to) according to several embodiments. The real modulator 1100 is an example of modulator 112 in Figure 1. The real modulator 1100 is configured to receive light 1102 from a local oscillator and to supply modulated light 1104 in response to light 1102 from the local oscillator. The real modulator 1100 is configured to split the input light into two paths, each path having a tunable optical time-of-flight delay. Two electronic modulator drive waveforms 1106, 1108 may be configured to cause a static optical time-of-flight delay at both branches given a nominal offset potential or current. The real modulator 1100 is then formed when the modulator waveforms are configured to cause a perturbation from this DC optical time-of-flight delay in a push-pull configuration (i.e., one perturbation is negative for the other). Such a real modulator 1100 may be used to mix a baseband sequence into the representation shown as the received waveform 1202 in Figure 12, and it can be seen that the sequence bandwidth is mixed with both positive and negative frequencies.

[0186] Figure 12 is a collection of plots 1200 illustrating digitization, mixing, filtering, and resampling performed on a received waveform 1202 in a non-limiting example. A modulated optical waveform is reflected from the system under test and, after interference from the local oscillator's light, the received waveform 1202, as illustrated in Figure 12, is received. The original sequence (or a superposition of sequences at different optical time-of-flight delays for elements along the system under test) can be recovered through various means used when the signal is mixed to the baseband, filtered, and optionally resampled before the sequence signal processing operations described above are performed. A non-limiting exemplary embodiment uses the Nyquist frequency f NyqThis may also include digitizing the received waveform 1202 using a sample rate higher than the highest signal frequency, resulting in a digitized received waveform 1204. This signal is then digitally mixed with a complex sine wave to form a mixed signal 1206, low-pass filtered to form a filtered signal 1208, and optionally resampled to form a resampled signal 1210. The digital signal processing operations according to various embodiments are then performed on the received signal to recover the phasors for each position along the system under test.

[0187] When using the Zadoff Chu sequence, the signal may be resampled so that the Nyquist frequency is within the bandwidth range of the sequence (Figure 12E) so that aliasing ensures that each optical time-of-flight position along the system under test is mapped to a unique frequency when the conjugate sequence is applied.

[0188] FIG. 13 is a diagram of one representation of a complex modulator 1300 according to some embodiments. The complex modulator 1300 is an example of the modulator 112 of FIG. 1. The complex modulator 1300 can also be used with a real receiver (e.g., the real receiver 1500 of FIG. 15). The complex modulator 1300 splits the incoming local oscillator light 1302 and sends the split light to two inner Mach-Zehnder (MZ) interferometers 1306, 1308, and combines the outputs of the inner MZ interferometers 1306, 1308 to the outer MZ interferometer 1310. The electric field of the outer (latter) MZ interferometer 1310 is used to make the outputs of the inner MZ interferometers 1306, 1308 in quadrature phase, and the inner MZ interferometers 1306, 1308 are supplied with the real and complex components of a sequence upmixed via a complex sine wave. After being mixed with the complex sine wave, as shown by the received waveform 1602 of FIG. 16, the entire spectrum of the sequence is either below or above DC. The basic operations after modulation and mixing with the complex sine wave include sampling the signal, mixing the signal back to baseband, low-pass filtering, and optionally resampling the signal.

[0189] FIG. 14 is a diagram of one representation of a complex receiver 1400 according to some embodiments. The complex receiver 1400 is similar to the receiver 140 of FIG. 1. For example, the complex receiver 1400 includes photodetectors 1402, 1404 and an optical hybrid 1406 similar to the photodetectors 106, 108 and optical hybrid 110 of FIG. 1. The complex receiver is configured to receive local oscillator light 1408 and light 1410 from the system under test.

[0190] Figure 15 shows one representation of the actual receiver 1500 according to several embodiments. The actual receiver 1500 may be used in the measurement system 100 of Figure 1 instead of the receiver 140 of Figure 1, which is exemplified as a complex receiver similar to the complex receiver 1400 of Figure 14. However, unlike the complex receiver 1400, which utilizes a quarter-wave delay λ / 4 to form an optical 90° hybrid, the actual receiver 1500, as shown in Figure 15 (a non-limiting example), utilizes a single coupler 1502 to interfere the local oscillator light 1504 and the system under test light 1506.

[0191] Figure 16 is a collection of plots 1600 illustrating digitization, mixing, filtering, and resampling performed on a received waveform 1602, in a non-limiting example. Plot 1600 includes the received waveform 1602, the digitized waveform 1604, the mixed signal 1606, the filtered signal 1608, and the resampled signal 1610. The interfering light 1604 in Figure 16 depicts the signal after interference by a real receiver 1500. The resulting real signal may be digitized using an analog-to-digital converter and mixed with a complex sine wave to mix either signal into the baseband. The mixed signal 1606 shows the positive frequency sequence spectrum mixed into the baseband. Low-pass filtering then yields the filtered signal 1608, after which normal sequence processing may be performed. The signal may optionally be resampled (resampled signal 1610) to facilitate signal processing in the various embodiments presented. Figure 16 shows the processing flow in which the actual receiver 1500 (Figure 15) is used, but the complex receiver 1400 (Figure 14) can also be used instead.

[0192] In fact, various different embodiments are contemplated herein. For example, a real modulator or a complex modulator may be used with a real receiver or a complex receiver. Sequences may be transmitted as baseband, up, down, or up / down mixed signals. One or more signals may be bandpass filtered instead of being mixed into the baseband and then lowpass filtered. One or more signals may be processed in the analog domain or digitized (sampled), and may also be processed in the digital domain.

[0193] Figure 17 is a functional flowchart of a signal processing scheme 1700 suitable for use with a real modulator (e.g., real modulator 1100 in Figure 11) and a real receiver (e.g., real receiver 1500 in Figure 15). A sequence is generated, the Fourier transform 1720 of the sequence is performed, and the complex conjugate 1722 of the Fourier-transformed sequence can be determined. As shown in Figure 17, a sine wave of the appropriate frequency is generated in digital logic 1702, used to mix the generated sequence 1704 for transmission to the real modulator, and to mix the input received data from the real modulator 1706. Filtering 1708 follows the mixing 1706 operation on the received signal. Optional resampling 1710 is performed on the sequence before mixing 1704 in the modulation path, and optional resampling 1712 is performed after filtering 1708 in the receiving path. A Fourier transform 1724 of the filtered and optionally resampled received data can be performed. A Fourier transform 1726 is performed on the product of the result of the complex conjugate 1722 and the result of the Fourier transform 1724. The resulting signal is a phasor-delay vector 1728.

[0194] In operations 1714 and 1716, respectively, the signal processing scheme 1700 includes, for example, converting a sequence from a digital representation to an analog representation via a digital-to-analog converter. The sequence can be transmitted as a common-phase component of a modulated signal (for example, modulated signal 138 in Figure 1).

[0195] Polarization-resolved sensing methods can be configured to resolve the orthogonal polarization components at each position along the system under test with respect to a single polarization reference in the system. Polarization-resolved sensing means that independent magnitude and phase measurements can be distinguished for each of two orthogonal polarization states (SoPs) with respect to a set of orthogonal reference polarization states for each position along the system under test. While any orthogonal states may be supported, the direct choice of orthogonal SoPs is perpendicular and in-plane linear polarization, commonly referred to as the S state and the P state.

[0196] Polarization-resolved OCoDR sensing utilizes a system architecture in which the system under test is illuminated with linearly polarized light from a laser, and the response to the incident light in two polarization states is independently resolved. The orthogonal SoP is defined by a component of a dual-polarization receiver, such as a polarization beam splitter.

[0197] Figure 18 shows one representation of a dual-polarization complex receiver 1800 according to several embodiments. The dual-polarization complex receiver 1800 splits linearly polarized local oscillator light 1802 into two paths via a beam splitter 1804 (BS 1804), rotates one path 1806 (ROT 1806), and as a result a pair of fields having orthogonal SoPs. The dual-polarization complex receiver 1800 also includes a polarizing beam splitter 1808 (PBS 1808) that splits the system light 1810 under test into two orthogonal linear SoPs. In this example, PBS 1808 forms a receiver polarization reference for the system. Each PBS output is interfered with the copolarized local oscillator light (from local oscillator light 1802) and converted into an electrical signal via one or more detectors specific to each SoP (e.g., photodetectors 1812, 1814, 1816, and 1818), recovering an independent signal—one for each orthogonal SoP. The complex bipolarized receiver shown in Figure 18 generates two complex interferograms—one for each orthogonal SoP.

[0198] Other options for orthogonal SoPs are also contemplated herein, including left-hand and right-hand circularly polarized light, or any other set of orthogonal SoPs.

[0199] To accommodate the dual-polarization complex receiver 1800, the digital subsystem may include additional analog-to-digital converters, acquisition circuits and / or logic, as well as signal processing logic for converting additional channels to digital format and applying the same signal processing to each SoP.

[0200] After signal processing is performed according to various embodiments disclosed herein, the result is two complex vectors representing two orthogonal SoPs. The magnitude of the traces represents the reflectivity of a given feature at a given position in the system under test within the orthogonal SoPs. The phase of the traces represents the optical time of flight (or its change) for each SoP.

[0201] Polarization diversity sensing refers to a system architecture in which the system under test is illuminated by two quadrature modulator systems of power (SoPs), and the responses at two quadrature receiver SoPs are resolved independently for each of the two quadrature modulator SoPs. Exemplary embodiments of signal separation for quadrature emitter SoPs include time-division multiplexing (TDM) and simultaneous quadrature polarization illumination. TDM quadrature SoP illumination and reception involve the use of optical switches or shutters to align the quadrature SoPs with respect to time.

[0202] Figure 19 is a diagram of one representation of a dual-polarization complex modulator 1900 according to several embodiments. The dual-polarization complex modulator 1900 is an example of modulator 112 in Figure 1. Simultaneous orthogonal SoP illumination and reception provide the advantage of continuous polarization diversity measurement. Linearly polarized input local oscillator light 1902 is split via beam splitter 1904 (BS 1904), one branch is rotated 1906 (ROT 1906), generating orthogonal SoPs in a second path, and a complex modulator for each SoP gives a complex sequence on each SoP before each output is combined into a single output via polarization beam combiner 1908 (PBC 1908), resulting in modulated light 1910.

[0203] Figure 20 is a functional flowchart for a signal processing scheme 2000 suitable for use with a polarization diversity OCoDR embodiment. The signal processing scheme 2000 includes generating a sequence 2002. A Fourier transform 2050 may be performed on the generated sequence, and a complex conjugate operation 2052 may be performed on the transformed sequence. The generated sequence is also sent to the S-polarized and P-polarized (or any two orthogonal SoP) inputs of a dual-polarized complex modulator (e.g., dual-polarized complex modulator 1900 in Figure 19). The delay difference 2004 of K samples is given to the sequence sent to one SoP with respect to the sequence sent to the orthogonal SoP. The generated sequence can be transformed from a continuous stream of complex numbers into its real part 2012 and imaginary part 2010. The delayed version of the generated sequence can be transformed into its real part 2018 and imaginary part 2020.

[0204] In operations 2022 and 2024, respectively, the signal processing scheme 2000 includes converting the real and imaginary parts of the sequence from their digital representations to their analog representations, for example, via a digital-to-analog converter. The real part 2012 may be transmitted as the common-mode component of the nominal-modulated signal 2030, and the imaginary part 2014 may be transmitted as the quadrature-phase component of the nominal-modulated signal 2030. Similarly, in operations 2026 and 2028, respectively, the signal processing scheme 2000 includes converting the real and imaginary parts of the delayed sequence from their digital representations to their analog representations. The real part 2018 may be transmitted as the common-mode component of the quadrature-modulated signal 2032, and the imaginary part 2020 may be transmitted as the quadrature-modulated signal 2030. The nominal-SoP-modulated signal 2030 and the quadrature-SoP-modulated signal 2032 may be provided to a modulator (for example, the bipolar complex modulator 1900 in Figure 19).

[0205] Signal processing scheme 2000 also includes, in operations 2034 and 2036, converting the phase and quadrature components of the nominal measurement signal 2006 from analog to digital, respectively. Signal processing scheme 2000 also includes converting the in-phase and quadrature components of the continuous interferogram into a continuous stream of complex numbers that are converted using the Fourier transform 2046. The converted stream of complex numbers is multiplied by a complex conjugate-transformed sequence from a complex conjugate operation 2052, and the Fourier transform 2054 may be performed to provide a phasor-to-delay vector 2056 for the nominal receiver SoP.

[0206] Similarly, in operations 2040 and 2042, the signal processing scheme 2000 includes converting the phase component and quadrature phase component from the quadrature measurement signal 2008 from analog to digital, respectively. The signal processing scheme 2000 further includes converting the in-phase and quadrature phase components of the continuous interferogram into a continuous stream of complex numbers that are converted using the Fourier transform 2048. The converted stream of complex numbers is multiplied by a complex conjugate-transformed sequence from the complex conjugate operation 2052, and the Fourier transform 2058 may be performed to provide a phasor-to-delay vector 2060 for the quadrature receiver SoP.

[0207] Other operations are performed according to the various embodiments presented herein. In some embodiments, it may be beneficial to double the sequence length with respect to the optical path length of the desired system under test so that K is effectively set to half the sequence length. When signal processing is performed according to the various embodiments and the phasor vectors are recovered, one region of the vector space will contain phasors resulting from one emission SoP (defined by a bipolarization modulator), while another region of the vector space will contain phasors resulting from orthogonal emission SoPs. The sequence length and / or parameter K can be tuned to ensure that desired features in the orthogonal SoPs occupy specific positions in the phasor vectors.

[0208] By using a dual-polarization receiver together with a dual-polarization modulator, four independent signals are received—two orthogonal emission SoPs identified by two orthogonal receiving SoPs. These four signals can be used to estimate the physical path length or path length difference in response to environmental perturbations (e.g., temperature, strain, vibration) of the system under test, with its sensitivity to perturbations of the polarization transfer function suppressed. Alternatively, these signals can be used to measure the polarization generation of the system under test over space and time, suppressing the effects of environmental perturbations.

[0209] This approach has the advantage of simultaneously detecting and separating the state of the system under test in response to each orthogonal polarization state, and irradiating the system under test simultaneously with the orthogonal incident polarization state. Subsequently, an independent analysis of the system under test's response may be performed for one or both orthogonal states, and additional conditions of the system under test, such as slow / fast axis orientation, birefringence, transverse forces, and others, can be estimated as a function of time and position along the system under test.

[0210] Figure 21 is a plot showing an example of a PRBS sequence 2100 according to several embodiments. The PRBS sequence 2100 has a length of 7 and contains values ​​in the set {+1, -1}. Referring together to Figures 1 and 21, the modulation signal source 114 may be configured to output a modulation signal 138 that exhibits autocorrelation, which is 1 at zero delay time and approaches zero at other delays. PRBS are special binary sequences (i.e., having two values, in this case +1 and -1) that appear random but can actually be easily computed and replicated.

[0211] PRBS exhibits a cyclic autocorrelation, being 1 at zero delay time and approaching zero at other delays. Specifically, for length N=2 m A maximum length PRBS of -1 exhibits an autocorrelation of 1 at zero delay and -1 / N at all (non-periodic) delay times outside of zero chip time, where 1 chip time is the atomic time unit (i.e., sample time) of the PRBS, and the PRBS contains N chips. An example of a PRBS sequence 2100 with length N=7 is shown in Figure 21. The cyclic autocorrelation of this PRBS sequence 2100 is shown in Figure 22.

[0212] Figure 22 is a plot illustrating the cyclic autocorrelation 2200 of the PRBS sequence 2100 in Figure 21. Figure 22 shows an autocorrelation value of 1 at delay time 0 (and even multiples of the sequence length), and values ​​of -1 / 7 at all other delay times. In some embodiments, instead of that sequence, a complex signal from the receiver may be complex-conjugated.

[0213] Figure 23 shows plots of the interferogram signal 2300 according to several embodiments. Other modulation means may be used to achieve reflector identification according to this disclosure. For example, instead of a phase modulator, a Mach-Zehnder modulator may be used in a push-pull configuration, thereby modulating the phase of one branch by π radians with respect to the other branch to achieve the desired phase relationship. In this case, the phasor traverses the unit circle, passing directly through the origin rather than along the circumference of the unit circle. A Mach-Zehnder modulator configured for two-phase shift modulation (BPSK) will achieve the desired modulation.

[0214] A phase modulator may be used to provide the PRBS signal (e.g., the modulated signal 138 in Figure 1 in some embodiments) to the incident EM radiation 124. The phase modulator may be used to modulate the incident EM radiation 124, which is then subjected to interference with the reference EM radiation 130 for a single sensor. In this case, as the input signal to the phase modulator is moved from one symbol nominally 0° to the other symbol 180°, a set of perpendicular phase waveforms traversing the circumference of a unit circle is obtained from the receiver. This is shown in Figure 23, where the symbols are represented by two points and the crossing between the symbols is indicated by a solid arrow. This figure shows that when a phase modulator is used, there is a continuity of phase as the output traverses from one symbol to the other, but the amplitude is constant.

[0215] Figure 23 shows cross-sections of the interferogram signals (x and y signals forming a quadrature phase) between the 0° symbol and the 180° symbol (solid arrows) and between 0° and -180° (dotted arrows). Both symbols are offset by the optical phase angle ψ. One method for calculating the PRBS is through the use of a linear feedback shift register (LFSR). The maximum length PRBS can be formed using an LFSR with register length m. As m increases, the value of the non-1 autocorrelation function of -1 / N becomes 1 / 2 m It asymptotically approaches zero.

[0216] The modulator 112 in Figure 1 may be supplied with a radio frequency (RF) electrical signal whose value forms a PRBS with integer chip times. When this signal is superimposed on the incident EM radiation 124 before being supplied to the sensor network (e.g., the system under test 116 in Figure 1), individual reflectors in the sensor network reflect this signal with their own inherent delays. For example, a reflector 10 meters along the sensor network will reflect the PRBS signal with a nominal delay of substantially 100 ns (given a dual-path optical time-of-flight delay of substantially 10 ns / m in the optical fiber), while a reflector 20 meters along the sensor network will reflect the PRBS signal with a delay of substantially 200 ns. If the PRBS chip time is, for example, 10 ns (e.g., a PRBS chip rate of 100 MCps), the PRBS signal reflected at 20 m will lag 10 chips behind the PRBS waveform reflected from the 10 m element.

[0217] Since the receiver output is AC coupled, iteration may be performed between symbols at +180° and -180° to adequately recover the amplitude. The symbols at 180° and -180° are the same, but their crossovers are different. The crossover to the -180° symbol is shown as a dotted arrow in Figure 12. Given the limitations of the waveform generator, it may be difficult to iterate symbol by symbol between the +180° and -180° symbols. Therefore, iteration may be performed based on a sequence, which is sufficient to allow for amplitude recovery despite the AC coupling of the signal.

[0218] A drawback of using a phase modulator is that, at most phase offsets, the x and y components of the signal have sharp points of change when the symbol is traversed.

[0219] Figure 24 is a plot illustrating the amplitudes of the x-component 2402 and y-component 2404 of the interferogram signal in several embodiments. Figure 24 shows the x-component 2402 and y-component 2404 of the crossover from 0° to 180° and in reverse using a phase modulator approach for ψ=25°. Figure 24 shows the x-component 2402 and y-component 2404 of the signal when symbols 0°, 180°, 0°, 180° are crossed, given the angular offset shown in Figure 23. A wider bandwidth is required to represent the real and imaginary signals due to the sharp transitions. This is a drawback, as the bandwidth of the received signal should be 2 to 3 times the chip rate in order to properly recover the signal. A disadvantage of using a phase modulator is that, for most phase offsets, the x-component and y-component of the signal have sharp turning points when symbols are crossed.

[0220] In some embodiments, complex amplitude modulation can be used with a Mach-Zehnder (MZ) modulator—that is, a splitter—followed by two phase modulation paths, and then a combiner. In the basic configuration, there are two phase modulation inputs to the modulator. When the same signal is supplied to both, the MZ modulator becomes a phase modulator. When opposite signals are supplied to each, the MZ modulator becomes an amplitude modulator. π Apply bias and set the input from 0 to 2V π By modulating across the range, the amplitude can be modulated to +1 and -1 states (for example, +1 at 180°), as shown in Figure 25.

[0221] Figure 25 is a plot illustrating the crossing of the interferogram signal 2500 (x and y signals forming a perpendicular phase) between a symbol at 0° and a symbol at 180° (solid arrows) according to several embodiments. The result of using an MZ modulator for amplitude modulation is that when the signal is crossed from one symbol to the other, the phase of the signal is either 0° or 180°, but the amplitude is continuous. This is suitable for OCoDR because, when the crossing amplitude trajectory is symmetric, the trajectory signal between symbols always has either a 0° or 180° phase, resulting in good cancellation of untuned sensors.

[0222] Another advantage of this method is that when the modulator input signal changes linearly from one symbol to the other, the amplitude changes sinusoidally, and the x and y components of the signal do not have additional high-frequency components. Figure 26 shows the x and y components of the signal when symbols 0°, 180°, 0°, and 180° are traversed, given the angular offset shown in Figure 25.

[0223] Figure 26 is a plot illustrating the x-components 2602 and y-components 2604 of the cross-section from 0° to 180° and inversely, using an MZ modulator approach for ψ=25° according to several embodiments. The x-components 2602 and y-components 2604 are sine waves, and no high-frequency components are needed to represent them. The x-components 2602 and y-components 2604 are in phase, whereas in Figure 24, the x-components 2402 and y-components 2404 are in phase.

[0224] The x-components 2602 and y-components 2604 of the interferogram have a functional form similar to the MZ modulator drive signal and do not occupy a wider bandwidth. Instead of requiring two to three times the bandwidth of the modulator drive bandwidth to represent the received signal in the case of a phase modulator, an MZ modulator may be used, requiring only a bandwidth similar to the drive bandwidth. As a non-restrictive example, a rooted cosine (RRC) filter with a β parameter of 1 may be used, resulting in an occupied bandwidth of twice the chip rate. The required sample rate is also twice the chip rate. It may also be possible to reduce the β parameter and reduce the extra bandwidth accordingly so that the required bandwidth is substantially close to 1.2 times the chip rate.

[0225] Another advantage of using MZ modulators is that the devices can be manufactured in a push-pull drive configuration, i.e., ±V π Modulations exceeding this range are derived from two differential inputs, and therefore each within the range of ±V. π It only needs to swing over 2. As a non-restrictive example, a modulator is V π This can be interpreted as =3.5, and therefore each output should only swing by ±1.75 volts.

[0226] Telecommunications components are designed and available for BPSK, QPSK, 16QAM, and higher-order modulation. Many components are designed to have two MZ modulators offset by 90 degrees to form a quadrature-phase modulator. A quadrature-phase modulator can be used by the various embodiments described above to generate a complex-value sequence of the modulated signal 138 according to, for example, CAZAC (including Zadoff Chu), ZACZ, or other complex-value sequences. Many are also designed with one modulator set to S-polarization and the other modulator set to P-polarization.

[0227] Figure 27 is a side view of an example of an optical fiber 2702. The OCoDR measures the change in the time of flight of light to a reflector (such as a scattering center) along the system under test. Sensing can be achieved via a fiber Bragg grating, a partial reflector, Rayleigh backscattering, or other backreflection or backscattering mechanisms. Figure 27 shows incident radiation 2704 in the optical fiber 2702 incident on the FBG or scattering center 2708 (depicted as three dots within the fiber core 2706). Some of the light is transmitted as transmitted light 2710, and some of the light (usually smaller) is reflected as reflected light 2712. Several embodiments disclosed herein allow for the measurement of the difference in the time of flight of light between a local oscillator path and the system under test path. By substantially isolating (or tracking) the local oscillator path such that the time of flight of light in the local oscillator (or reference) path is substantially constant (or known), the change in the time of flight of light along the system under test path to any given reflector can be measured. For example, if a reflective element (e.g., scattering center 1608) in Figure 27 is attached to a vibrating substrate, these vibrations can cause changes in the time of flight of light in the path to and from the reflector. The equivalent change in mechanical path length can be estimated to the order of 1 nm or more using some embodiments disclosed herein. As a result, vibrations with corresponding mechanical displacements of ~1 nm (or more) can be resolved using the embodiments disclosed herein. Similarly, cumulative strain and / or temperature in the path of the system under test can cause changes in the refractive index and / or physical path length of the system medium under test. Changes in temperature and / or strain in the path of the system under test to a given reflective element can be monitored by monitoring and integrating (i.e., unwrapping) the phase of an interferometric phasor corresponding to a given reflective element.

[0228] Figure 28 shows another example of optical fiber 2802. In the example shown in Figure 28, two FBGs 2804 and 2806 can be used as partial reflectors. Shorter FBGs have the advantage of a wide response spectrum and therefore support a wide dynamic range of temperature and / or distortion (or other effects that can be converted into changes in optical path length). When two reflectors (e.g., scattering centers) are used, temperature and / or distortion measurements between the reflectors can be performed. This can be achieved by monitoring and unwrapping (i.e., integrating) the phases of the phasors corresponding to the two reflectors, and then subtracting the phase from one reflector from the phase of the other reflector. Such operation isolates the temperature and / or distortion effects that are solely attributable to the path between the two reflectors. For example, alternative equivalent mathematical operations can be performed, such as multiplying the phasor corresponding to the first reflecting element (e.g., FBG 2804) by the complex conjugate of another phasor corresponding to the second reflecting element (e.g., FBG 2806), and then unwrapping the phase of the product.

[0229] In the Zadoff-Chu sequence architecture 400 in Figure 4 (and other architectures including the frequency-domain architecture 300 in Figure 3), the Fourier transform output can encode a single reflector among multiple samples of the Fourier transform when the reflector is located at an optical time-of-flight delay that is not an even multiple of the reciprocal of the sample rate. In this case, the multiple samples can be used to estimate a single phasor with a higher SNR for a single phasor (i.e., a single complex transform domain sample) by performing a phase offset calibration in the nominal state, then aligning the multiple phasors (complex samples) to the same angle, and then adding the phasors together.

[0230] The optical path length within an optical fiber is sensitive to both strain and temperature. Temperature measurements can be performed by isolating the optical fiber from strain and monitoring the unwrapped phase difference from two reflective (scattering) elements along the system under test, converting the phase to temperature via a calibration constant. Strain measurements can be performed by placing a strain-insulated fiber, thermally coupled to a strain-coupled fiber, at the same location and subtracting the temperature-only measurement of the strain-insulated fiber from the strain-plus-temperature measurement of the strain-coupled fiber.

[0231] Figure 29 is a flowchart illustrating method 2900 for performing absolute measurements of a system under test according to several embodiments. As described above, OCoDR is capable of measuring changes in temperature or strain from a nominal state, the nominal state being the state at the start time when the phases of the interferometric phasors are integrated (i.e., unwrapped). Embodiments disclosed herein can be extended to absolute measurements by performing method 2900 schematically shown in Figure 29. In operation 2902, the phase difference of the interferometric phasors corresponding to two reflectors of interest is taken (i.e., the difference between one phasor and the other). In operation 2904, the difference of the results is unwrapped (tracked) over time. In operation 2906, a substantially fixed-frequency laser light source is used at a nominal frequency ν o From optical frequency ν o The laser is moved slowly up to +Δν, but does not necessarily have to be linear as long as the optical frequency moves through the change Δν. In some embodiments, moving a substantially fixed-frequency laser source from the nominal frequency to the optical frequency involves slowly (or linearly) tuning the substantially fixed-frequency laser to induce a zero (or known) Doppler shift in the Fourier transform position of the interferometric phasor for a given feature (the interferometric phasor is

[0232]

number

[0233] (Assuming that the change in ν results in an offset in the Fourier transform region of the reflector of interest). Rapid tuning of the laser is also possible when Doppler shift is given to be considered by adjusting the Fourier transform sample considered for a given reflector.

[0234] When the difference between two optical time-of-flight delays is taken as an interferometric phasor (i.e., a position along the system under test), the resulting phase is νΔτ d It is proportional to, and here,

[0235]

number

[0236] And,

[0237]

number

[0238]

number

[0239] These correspond to the two positions of interest. If the system under test is isolated from environmental perturbations for the time it takes for the laser to be tuned over Δν, the phase difference is Δψ d =2π(ν o +Δν)Δτ d -2πν o Δτ d =2πΔνΔτ d The total phase displacement Δψ given by d It can be traced (i.e., unwrapped or integrated) to obtain Δτ. With precise knowledge of Δν, the absolute time-of-flight difference between the two reflectors (scattering centers) of interest is Δτ d =2πΔν / Δψ dIt can be calculated as follows. Thus, in operation 2908, method 2900 includes calculating the absolute time-of-flight difference between two reflectors of interest. As a non-limiting example, Δτ at nominal temperature and / or strain. d By calibrating, the calibration Δτ d This is the current Δτ d This is compared with the absolute temperature and / or strain, thereby allowing for the estimation of the absolute temperature and / or strain.

[0240] In some embodiments, absolute temperature and / or strain (or other effects that translate to temperature and / or strain) may be measured by including a calibration reference structure similar to that shown in Figure 28. The calibration reference structure includes two reflectors (such as scattering centers) that are substantially isolated from temperature and / or strain (or coupled to a measuring device for measuring the temperature and / or strain acting on the calibration structure, i.e., a region of the system under test between the two reflectors). The reference calibration structure may be located at any location along the system under test.

[0241]

number

[0242] Another means of calibrating and estimating (where,

[0243]

number

[0244] (This is the time-of-flight difference of light between the reflective elements of the calibration structure.)

[0245]

number

[0246] This is used to obtain accurate measurements. A laser source of substantially fixed frequency is moved slowly (and sometimes faster) through a substantially known change in optical frequency Δν. As the laser is tuned over Δν, the difference in the interferometric phasor of the calibration structure is tracked, which is Δψ ref This is expressed as follows: The difference between any two interferometric phasors in the system under test subjected to temperature and / or strain (i.e., the measuring portion of the system under test opposite the calibration structure) is Δψ d It is expressed as follows. In this case, Δτ d The exact absolute measurement is,

[0247]

number

[0248] It can be obtained by taking [a certain action].

[0249] While the system under test is stationary (the time it takes to perform the calibration, i.e., the time it takes to move the laser over Δν), Δτ is applied to any desired pair of reflectors. d By performing absolute measurements and then following up with interferometric phasors, the dynamic relative measurements enabled by OCoDR can be correctly offset by absolute temperature (and / or strain, and / or any other effects that can be converted into changes in optical path length) to form dynamic absolute measurements that represent the average value measured over any desired segment of the system under test.

[0250] Those skilled in the art will understand that the functional elements (e.g., functions, operations, activities, processes, and / or methods) of the embodiments disclosed herein can be implemented in any suitable hardware, software, firmware, or combination thereof. Figure 30 illustrates non-limiting examples of implementations of the functional elements disclosed herein. In some embodiments, some or all of the functional elements disclosed herein can be implemented by hardware specifically configured to carry out the functional elements.

[0251] Figure 30 is a block diagram of a circuit 3000 that may be used in some embodiments to perform various functions, operations, activities, processes, and / or methods disclosed herein. The circuit 3000 includes one or more processors 3002 (sometimes referred to herein as "processor 3002") operably coupled to one or more data storage devices (sometimes referred to herein as "storage device 3004"). The storage 3004 includes machine-executable code 3006 stored thereon, and the processor 3002 includes logic circuit 3008. The machine-executable code 3006 includes information describing functional elements that may be implemented (e.g., executed) by the logic circuit 3008. The logic circuit 3008 is adapted to implement (e.g., execute) the functional elements described by the machine-executable code 3006. When the circuit 3000 executes the functional elements described by the machine-executable code 3006, it should be considered dedicated hardware configured to perform the functional elements disclosed herein. In some embodiments, the processor 3002 may be configured to execute the functional elements described by the machine-executable code 3006 sequentially, simultaneously (for example, on one or more different hardware platforms), or in one or more parallel process streams.

[0252] When implemented by the logic circuit 3008 of the processor 3002, the machine-executable code 3006 is configured to adapt the processor 3002 to perform the operations of the embodiments disclosed herein. For example, the machine-executable code 3006 may be configured to adapt the processor 3002 to perform at least some or all of the operations described with respect to the control circuit 104 of Figure 1, the modulated signal source 194 of Figure 1, the multiplier-accumulator architecture 200 of Figure 2, the frequency domain architecture 300 of Figure 3, the Zadoff-Chu sequence architecture 400 of Figure 4, the signal processing scheme 1700 of Figure 17, the signal processing scheme 2000 of Figure 20, and / or the method 2900 of Figure 29.

[0253] The processor 3002 may include a general-purpose processor, a dedicated processor, a central processing unit (CPU), a microcontroller, a programmable logic controller (PLC), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), a graphics processing unit (GPU), or other programmable logic devices, discrete gates or transistor logic, discrete hardware components, other programmable devices, or any combination thereof, designed to perform the functions disclosed herein. A general-purpose computer including a processor is considered a dedicated computer, while the general-purpose computer is configured to execute functional elements corresponding to machine-executable code 3006 (e.g., software code, firmware code, hardware description) relating to embodiments of the present disclosure. The general-purpose processor (which may be referred to herein as a host processor or simply a host) may be a microprocessor, but in alternative embodiments, the processor 3002 may include any conventional processor, controller, microcontroller, or state machine. The processor 3002 can also be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, multiple microprocessors, one or more microprocessors working in conjunction with a DSP core, or any other such configuration.

[0254] In some embodiments, the storage 3004 includes volatile data storage (e.g., random access memory (RAM)) and non-volatile data storage (e.g., flash memory, hard disk drive, solid-state drive, erasable programmable read-only memory (EPROM), etc.). In some embodiments, the processor 3002 and the storage 3004 may be implemented within a single device (e.g., a semiconductor device product, a system-on-a-chip (SoC), etc.). In some embodiments, the processor 3002 and the storage 3004 may be implemented in separate devices.

[0255] In some embodiments, the machine-executable code 3006 may include computer-readable instructions (e.g., software code, firmware code). In a non-limiting example, the computer-readable instructions may be stored in storage 3004, directly accessed by processor 3002, and executed by processor 3002 using at least logic circuitry 3008. Also, in a non-limiting example, the computer-readable instructions may be stored on storage 3004, transferred to a memory device (not shown) for execution, and executed by processor 3002 using at least logic circuitry 3008. Thus, in some embodiments, logic circuitry 3008 includes electrically configurable logic circuitry 3008.

[0256] In some embodiments, machine-executable code 3006 may describe hardware (e.g., circuits) implemented within logic circuits 3008 to execute functional elements. This hardware may be described at any of several levels of abstraction, from low-level transistor layouts to high-level description languages. High-level abstractions may use hardware description languages ​​(HDLs), such as the IEEE standard hardware description language (HDL). Non-limiting examples include Verilog®, SystemVerilog®, or Very Large-Scale Integrated (VLSI) Hardware Description Language (VHDL®).

[0257] An HDL description can be translated into a description at any level of abstraction among a number of other levels of abstraction as needed. As an unrestricted example, a high-level description can be translated into a logic-level description such as a register transfer-level (RTL), gate-level (GL), layout-level, or mask-level description. As an unrestricted example, the microoperations performed by the hardware logic circuitry of logic circuit 3008 (e.g., gates, flip-flops, registers, but not limited to these) can be described in RTL, then translated into a GL description by a synthesis tool, and the GL description can be translated by a place-and-route tool into a layout-level description corresponding to the physical layout of an integrated circuit of programmable logic devices, discrete gates or transistor logic, discrete hardware components, or combinations thereof. Thus, in some embodiments, machine-executable code 3006 may include HDL, RTL, GL descriptions, mask-level descriptions, other hardware descriptions, or any combination thereof.

[0258] In embodiments where the machine-executable code 3006 includes a hardware description (of any level of abstraction), the system (including storage 3004, not shown) may be configured to implement the hardware description described by the machine-executable code 3006. In a non-limiting example, the processor 3002 may include a programmable logic device (e.g., an FPGA or PLC), and the logic circuit 3008 may be electrically controlled to implement the circuit corresponding to the hardware description within the logic circuit 3008. Also in a non-limiting example, the logic circuit 3008 may include hardwired logic manufactured by a manufacturing system (including storage 3004, not shown) according to the hardware description of the machine-executable code 3006.

[0259] Regardless of whether the machine-executable code 3006 contains computer-readable instructions or hardware descriptions, the logic circuit 3008 is adapted to execute the functional elements described by the machine-executable code 3006 when implementing the functional elements of the machine-executable code 3006. Note that while hardware descriptions cannot directly describe functional elements, they indirectly describe the functional elements that the hardware elements described by the hardware descriptions can execute.

[0260] As used in this disclosure, the terms “module” or “component” may refer to a particular hardware implementation configured to perform the operation of a module or component and / or software object or software routine that is stored on and / or executed by general-purpose hardware of a computing system (e.g., computer-readable media, processing devices, etc.). In some embodiments, the different components, modules, engines, and services described in this disclosure may be implemented as objects or processes that run on a computing system (e.g., as separate threads). While some of the systems and methods described in this disclosure are generally described as being implemented in software (stored on and / or executed by general-purpose hardware), specific hardware implementations, or combinations of software and dedicated hardware implementations, are also possible and intended.

[0261] As used in this disclosure, the term “combination” referring to multiple elements may include combinations of all elements or various different subcombinations of some elements. For example, the phrase “A, B, C, D, or any combination thereof” may refer to any one of A, B, C, or D, any combination of A, B, C, and D, as well as any subcombination of A, B, C, or D such as combinations of A, B, and C, combinations of A, B, and D, combinations of A, C, and D, combinations of B, C, and D, combinations of A and B, combinations of A and C, combinations of A and D, combinations of B and C, or combinations of C and D.

[0262] The language used in this disclosure and in particular in the appended claims (for example, the text of the appended claims) is generally intended to be "unrestricted" language (for example, the phrase "includes" should be interpreted as "includes but not limited", the phrase "has" should be interpreted as "has at least have", and the phrase "includes" should be interpreted as "includes but not limited").

[0263] In addition, if a particular number of claim enumerations is intended to be introduced, such intention is explicitly stated in the claim; if there is no such enumeration, such intention does not exist. For example, to aid understanding, an appended claim may introduce a claim enumeration by including the introductory phrases “at least one” and “one or more.” However, even if such phrases are used in the original English text, the introduction of a claim enumeration with the indefinite article “a” or “an” should not be interpreted as meaning that a particular claim containing such an introduced claim enumeration is limited to embodiments that include only one such enumeration, even if the claim includes the introductory phrase “one or more” or “at least one” and an indefinite article such as “a” or “an” (for example, “a” and / or “an” should be interpreted as meaning “at least one” or “one or more”), and the same applies to the use of the definite article used to introduce a claim enumeration.

[0264] In addition, even if a specific number of claims are explicitly listed, a person skilled in the art will understand that such a list should be interpreted as meaning at least the number listed (for example, an unadorned list of "two lists" without any other modifiers means at least two lists, or two or more lists). Furthermore, in cases where idiomatic expressions similar to "at least one of A, B, and C, etc." or "one or more of A, B, and C, etc." are used, such constructions are generally intended to include A alone, B alone, C alone, A and B together, A and C together, B and C together, or A, B, and C together, etc.

[0265] Furthermore, any separate word or phrase indicating two or more alternative words, whether in a description, claim, or drawing, should be understood as construing the possibility of including one of the words, any of the words, or both of the words. For example, the phrase "A or B" should be understood to include the possibilities of "A" or "B" or "A and B".

[0266] While this disclosure has been described herein in relation to certain exemplary embodiments, those skilled in the art will recognize and understand that the invention is not so limited. Rather, many additions, deletions, and modifications to the exemplary embodiments described herein, along with their legal equivalents, can be made without departing from the scope of the invention as described in the claims. In addition, features from one embodiment can be combined with features from another embodiment while remaining included within the scope of the invention as intended by the inventors. [Explanation of symbols]

[0267] 100 Measurement Systems 102 EM Radiation Source 104 Control circuits 106 Photodetector 108 Photodetectors 110 Optical Hybrid 112 Modulator 114 Modulated signal source 116 Optical system 116 Systems under test 118 Optical Splitter 120 Light Circulator 122 Continuous wave EM radiation 126 Modulated EM radiation 128 Reflected EM Radiation 130 Reference EM Radiation 132 Splitter Inputs 134 First splitter output 136 Second splitter output 138 Modulated signal 140 Receiver 142 Interferential EM radiation 144 First input 146 Second input 148 First Output 150 Second output 152 Common-mode interference measurement output 154 Orthogonal Interferometry Output 156 First measurement signal 158 Second measurement signal 200 Multiplier-Accumulator Architecture 208 Latency Network 210 Actual Part 212 Imaginary part 218 Feather 300 frequency domain architecture 400 Zadoff-Chu Sequence Architecture 500 Phase Derivative 600 reflectance 602 First reflector 604 Second reflector 606 Third reflector 700 Phase derivative 702 First Phase Derivative 704 Second Phase Derivative 706 Third Phase Derivative 708 Reference Phase Derivative 800 Phase derivative 802 First Phase Derivative 804 Second Phase Derivative 806 Third Phase Derivative 897, 2237, and 3779 sequence sample placements 900 Phase derivative 902 First Phase Derivative 904 Second Phase Derivative 906 Third Phase Derivative 1000 Phase Modulator 1002 Light from the local oscillator 1004 Modulated light 1006 Waveguide 1100 Actual Modulator 1102 Light from a local oscillator 1106, 1108 Electronic modulator drive waveform 1200 plots 1202 Received waveform 1204 Received waveform 1300 Complex Modulator 1302 Incident light from local oscillator 1306, 1308 Internal Mach-Zehnder (MZ) interferometer 1310 External MZ Interferometer 1400 Complex Receiver 1402, 1404 Photodetectors 1406 Optical Hybrid 1408 Light from a local oscillator 1410 light 1500 Actual Receiver 1502 Single Coupler 1504 Light from a local oscillator 1506 Test System Optical 1600 Received waveform 1602 Plot 1602 Received waveform 1604 Digitized Waveform 1606 mixed signal 1608 Filtering signal 1610 Resampled signal 1700 Signal Processing Methods 1702 generation 1704 Mixed 1706 Mixed 1708 Filtering 1710 resampling 1712 resampling 1720 Fourier Transform 1722 Complex conjugate 1724 Fourier Transform 1726 Fourier Transform 1728 Phasar vs. Delay 1800 Dual Polarization Complex Receiver 1804 Beam Splitter 1806 ROT 1808 Polarizing Beam Splitter 1810 Test System Optical 1812, 1814, 1816, and 1818 photodetectors 1900 Dual Polarization Complex Modulator 1902 Linear Polarization Input Local Oscillator 1904 Beam Splitter 1906 ROT 1908 Polarizing Beam Combiner 1910 Modulated light 2000 Signal Processing Methods 2002 Sequence 2012 Practical Department 2014 Ikube 2018 Practical Department 2020 Ikube 2030 Nominal Modulated Signal 2030 Quadrature Modulated Signal 2032 Quadrature Modulated Signal 2046 Fourier Transform 2048 Fourier Transform 2050 Fourier Transform 2052 Complex conjugate operation 2054 Fourier Transform 2056 Phasor vs. Delay Vector 2058 Fourier Transform 2060 phasor vs. delay vector 2100 PRBS series (sequence) 2200 Cyclic Autocorrelation 2300 Interferogram signal 2402 x component 2404 y component 2500 interferogram signals 2602 x component 2604 y component 2702 Optical Fiber 2704 Incident radiation 2706 Fiber Core 2708 FBG or scattering center 2710 Transmitted light 2712 Reflected light 2802 Optical Fiber 2804 and 2806 FBG 2900 method 3000 circuits 3002 Processor 3004 Storage Devices 3006 Machine-executable code 3008 Logic Circuit 4096 sequence length

Claims

1. A device comprising a modulator and a receiver, The modulator is configured to receive incident electromagnetic radiation of substantially fixed frequency generated by one or more electromagnetic radiation sources, the incident electromagnetic radiation includes continuous wave electromagnetic radiation, and the modulator is configured to provide a sequence to the amplitude, phase, or both of the incident electromagnetic radiation to generate modulated electromagnetic radiation, the modulated electromagnetic radiation includes continuous wave electromagnetic radiation, The aforementioned receiver is, Receiving the substantially fixed frequency reference electromagnetic radiation generated by one or more electromagnetic radiation sources, wherein the reference electromagnetic radiation includes continuous wave electromagnetic radiation. Receiving reflected electromagnetic radiation from the optical system in response to the modulated electromagnetic radiation, To generate interference electromagnetic radiation in response to the aforementioned reference electromagnetic radiation and the aforementioned reflected electromagnetic radiation, To generate a continuous interferogram in response to the aforementioned interference electromagnetic radiation. A device configured to perform the following actions.

2. The apparatus according to claim 1, wherein the sequence includes a pseudorandom sequence, an autocorrelation sequence that is at least substantially zero, a constant amplitude zero correlation (CAZAC) sequence, or a Zadoff-Chu sequence.

3. The apparatus according to claim 1, wherein the optical system includes an optical fiber.

4. The apparatus according to claim 3, wherein the optical fiber includes one or more of the following: a fiber Bragg grating that reflects the modulated electromagnetic radiation at various positions within the optical fiber; a reflective element that reflects the modulated electromagnetic radiation at various positions within the optical fiber; and a manufacturing defect that backscatters the modulated electromagnetic radiation via Rayleigh scattering.

5. It is further equipped with a dual-polarization receiver, The aforementioned dual-polarization receiver is, The reflected electromagnetic radiation from the optical system under test is divided into a first field component corresponding to the nominal polarization state and a second field component corresponding to the orthogonal polarization state, The first and second field components are interfered with copolarized local oscillator light to form two interferograms. It is configured to do the following: The apparatus according to claim 1, wherein the two interferograms represent the response of the optical system to the nominal polarization state and the orthogonal polarization state, respectively.

6. Furthermore, equipped with a dual polarization modulator, The aforementioned dual polarization modulator is Dividing the incident local oscillator light into two fields, The phase, amplitude, or both of the phase and amplitude of light in each of the two fields is independently modulated by the respective real electrical signal or complex electrical signal. The first field is composed of nominally polarized states, and the second superimposed field is composed of orthogonally polarized states. These two fields are coupled into a single optical output field. It is configured to do the following: The apparatus according to claim 1, wherein the electrical signals driving the two fields include the same substantially zero autocorrelation sequence, the same substantially zero autocorrelation sequence driving the nominal polarization state is delayed with respect to the same substantially zero autocorrelation sequence driving the orthogonal polarization state, and the signal-processed vector includes one or more regions of the optical system responding to the nominal polarization state and one or more second regions of the system under test responding to the orthogonal polarization state.

7. The apparatus according to claim 1, further comprising a control circuit configured to apply either the sequence or the complex conjugate of the sequence to a digitized version of the continuous interferogram in order to extract phasors corresponding to different optical time-of-flight delays.

8. The apparatus according to claim 7, wherein the control circuit is configured to sense at least one of a change in the optical path length of the optical system or any effect that is converted into a change in the optical path length in response to the phasor.

9. The apparatus according to claim 8, wherein the change in optical path length sensed by the control circuit includes one or more of the following: a distortion acting on the optical system, the temperature of the optical system, and a lateral force acting on the optical system.

10. A device comprising a receiver and a control circuit, The aforementioned receiver is, The generation of interfering electromagnetic radiation in response to reference electromagnetic radiation and reflected electromagnetic radiation, wherein the reflected electromagnetic radiation is received from the system under test in response to modulated electromagnetic radiation supplied to the system under test, and the reference electromagnetic radiation and the modulated electromagnetic radiation include continuous wave electromagnetic radiation. To generate a continuous interferogram in response to the aforementioned interference electromagnetic radiation. It is configured to do the following: The aforementioned control circuit is To generate the aforementioned modulated electromagnetic radiation, a sequence is supplied to the modulated signal source in response to the incident electromagnetic radiation, To obtain a digitized continuous interferogram, the continuous interferogram is digitized, Extracting phasors corresponding to different delays in response to applying one of the sequence or its complex conjugate to the digitized continuous interferogram. A device configured to perform the following actions.

11. A method for performing optical code delay reflectance measurement (OCoDR), A step of modulating a sequence on incident electromagnetic radiation in order to obtain modulated electromagnetic radiation, wherein the sequence has at least substantially zero cyclic autocorrelation with respect to a non-zero shift of the sequence, The steps include injecting the modulated electromagnetic radiation into the system under test, Steps include interfering reflected electromagnetic radiation received from the system under test in response to modulated electromagnetic radiation with reference electromagnetic radiation in order to obtain interfering electromagnetic radiation, wherein the reference electromagnetic radiation includes continuous wave electromagnetic radiation of substantially fixed frequency; The steps include converting the aforementioned interference electromagnetic radiation into an electrical signal, The steps include: digitizing the electrical signal in order to obtain a digitized continuous interferogram; A method comprising the step of applying one of the sequence or the complex conjugate of the sequence to the digitized continuous interferogram in order to obtain phasors corresponding to different delays.

12. The step of applying one of the sequence or the complex conjugate of the sequence to the digitized continuous interferogram is: The steps include multiplying the digitized continuous interferogram by various cyclically shifted or time-shifted copies of the sequence in order to obtain the product, The method according to claim 11, comprising the step of summing the products over the sequence length of the sequence in order to recover the phasor.

13. The method according to claim 12, wherein the amplitude of the phasor substantially corresponds to the amplitude of the reflected electromagnetic radiation at a position in the system under test that is proportional to the shift of the sequence.

14. The method according to claim 12, wherein the phase of the phasor substantially corresponds to the optical time-of-flight delay or delay change of the system under test at a position within the system under test that is proportional to the shift of the sequence.

15. The step of applying one of the sequence or the complex conjugate of the sequence to the digitized continuous interferogram is: A step of estimating the frequency domain representation of the sequence, The steps include: estimating the frequency domain representation of the digitized continuous interferogram; The steps of complex conjugating either the frequency domain representation of the sequence or the frequency domain representation of the digitized continuous interferogram, The steps of obtaining the product include multiplying the complex conjugate of one of the frequency domain representations of the sequence and the frequency domain representation of the digitized continuous interferogram by the other of the frequency domain representations of the sequence and the frequency domain representation of the digitized continuous interferogram, The method according to claim 11, comprising the step of estimating the inverse frequency domain representation of the product in order to obtain the phasor vector.

16. A method for performing optical code delay reflectance measurement (OCoDR), A step of modulating a Zadoff-Chu sequence on an incident electromagnetic radiation in order to obtain modulated electromagnetic radiation, wherein the incident electromagnetic radiation and the modulated electromagnetic radiation include continuous wave electromagnetic radiation, The steps include injecting the modulated electromagnetic radiation into the optical fiber, The steps of interfering the reflected electromagnetic radiation received from the optical fiber in response to the modulated electromagnetic radiation with the reference electromagnetic radiation in order to generate interference electromagnetic radiation, The steps include converting the aforementioned interference electromagnetic radiation into an electrical signal including an interferogram, The steps include: digitizing the electrical signal in order to generate a digitized interferogram; The steps include determining the complex conjugate of either the Zadoff-Chu sequence or the digitized interferogram, The steps include multiplying the complex conjugate of one of the Zadoff-Chu sequence or the digitized interferogram by the other of the Zadoff-Chu sequence or the digitized interferogram in order to generate a product, A method comprising the step of determining the frequency domain representation of the product in order to recover the phasor vector.

17. The method according to claim 16, wherein the frequency domain representation is taken over a number of samples smaller than the length of the Zadoff-Chu sequence, and produces an output sample rate faster than the reciprocal of the optical time-of-flight delay corresponding to the length of the Zadoff-Chu sequence.

18. The method according to claim 17, wherein the amplitude of the phasor corresponds to the amplitude of the back-reflected signal at a position in the optical fiber that is proportional to the shift of the Zadoff-Chu sequence.

19. The method according to claim 17, wherein the phase of the phasor corresponds to the optical time-of-flight delay or delay change of the optical fiber at a position in the optical fiber that is proportional to the shift of the Zadoff-Chu sequence.

20. The optical fiber is A fiber Bragg grating that reflects the modulated electromagnetic radiation at various positions within the optical fiber, A reflective element that reflects the modulated electromagnetic radiation at various positions within the optical fiber, Defects exhibiting Rayleigh scattering, which causes the modulated electromagnetic radiation to backscatter within the optical fiber. The method according to claim 17, comprising one or more of the above.

21. The method according to claim 17, further comprising the step of estimating the state of the optical fiber based on the amplitude, phase, or both of the vector of the phasor.

22. The method according to claim 21, wherein the step of estimating the state includes the step of estimating one or more of the following: birefringence, temperature, strain, or any effect that is converted into the birefringence, temperature, or strain.

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